Skip to main content

Full text of "The Philosophical magazine; a journal of theoretical, experimental and applied physics"

See other formats























RICHARD TAYLOR, F.L.S. G.S. Astr.S. Nat.H.Mosc.&c. 

" Nee aranearum sane textus ideo melior quia ex se fila gignunt, nee noster 
vilior quia ex alienis libamus ut apes." Just. Lips. Polit. lib. i. cap. 1 . Not. 






Printers and Publishers t (J the University of London ; 


AND CO.; s. highley; whittakek and co.; and sherwood, 





" MecHtationis est perscrutari occulta; contemplationis est adniirari 

perspicua Admiratio general quaestionem, qiiaestio investigationem, 

investigatio inventionem." — Hugo de S. Victore. 

— " Cur Spirent venti, cur terra dehiscat. 
Cur mare turgescat, pelago cur tantus amaror, 
Cur caput obscura Phoebus ferrugine condat, 
Quid toties diros cogat flagrare cometas ; 
Quid pariat nubes, veniant cur fulmina coelo. 
Quo micet igne Iris, superos quis conciat orbes 
Tarn vario motu." 

J. B. Pinelli ad Mazonium. 






Messrs. J. Tyndall and H. Knoblauch's Second Memoir on the 
Magneto-optic Properties of Crystals, and the relation of Mag- 
netism and Diamagnetism to Molecular Arrangement 1 

Mr. .1. Bryce's Notices of a late "V^isit to the Parallel Roads of 

Lochaber .33 

Dr. Buys Ballot on the great importance of Deviations from the 
mean state of the Atmosphere for the Science of Meteor- 
ology 42 

Mr. A. Cayley on the Triadic Arrangements of Seven and Fif- 
teen Things 50 

Prof. W. Thomson on some remarkable effects of Lightning, 
observed in a Farm-house near Moniemail, near Cupar-Fife 53 

Proceedings of the Royal Society 57 

Cambridge Philosophical Society 68 

■ Royal Astronomical Society 69 

■ British Meteorological Society 71 

The Lagoons of Tuscany 72 

On the Interpretation of Mariotte's Law, by Lieut. E. B. Hunt, 

U.S. Corps of Engineers 76 

Effects of Atmospheric Electricity upon the Wires of the Mag- 
netic Telegraph 78 

Meteorological Observations for May 1850 79 

Meteorological Observations made by Mr. Thompson at the 
Garden of the Horticultural Society at Chiswick, near 
London ; by Mr. Veall at Boston ; by the Rev. W. Dunbar at 
Api^legarth Manse, Dumfries-shire ; and by the Rev. C. 
Clouston at Sand wick Manse, Orkney , 80 


Prof. Potter on the Aeroraetric Balance, an instrument for mea- 
suring the Density of the Air in which it is situated 81 



Dr. Faraday s Exiierimontal Researches in Electricity. — Twenty- 
third Series : — On the {H)hir or other condition of diamagnetic 
bodies 88 

Mr. W. Spottiswoode on the Geometrical Interpretation of Qua- 
ternions 108 

Mr. J. Buckman on the Structure and Arrangement of the Tes- 
serae in a Roman pavement discovered at Cirencester in 
August 1849 119 

Prof. \V. Thomson on the Effect of Pressure in Lowering the 
Freezing- Point of Water experimentally demonstrated .... 123 

Mr. J. P. Joule on a remarkable ajipearance of Lightning .... 127 

Mr, J. Glaishcr's Remarks on the Weather during the Quarter 
ending June 30, 1850 129 

Notices respecting New Books : — Dr. Anderson's Course of 
Creation 145 

Proceedings of the Cambridge Philosophical Society 146 

Chemical Examination of a Mineral containing Oxide of Ura- 
nium, from the north shore of Lake Superior, by J. D.Whitney 153 

On the Dust- Storms of India, by P. Baddeley, Esq 155 

On certain phienomena of forced Dilatation of Liquids, by M. 
Marcellin Berthelot 158 

Meteorological Observations for June 1850 159 

Table 160 


Dr. Percy on the Composition of Beudantite 161 

The Rev. T. P. Kirkman on the Triads made with Fifteen 

Things 169 

Mr. D. Campbell on the Action of the Soap-Test upon Water 
containing a Salt of Magnesia only, and likewise upon Water 

containing a Salt of Magnesia and a Salt of Lime 171 

Mr. J. Middleton on an Accelerating Process in Photography 178 

Mr. R. Crossley on Algerite, a new Mineral Species. 179 

Prof. Graham on the Diffusion of Liquids 181 

Mr. T. S. Davies on Geometry and Geometers. No. VI 198 

Mr. J. J. Sylvester on an Instantaneous Demonstration of Pas- 
cal's Theorem by the method of Indeterminate Coordinates 212 
Mr. J. J. Sylvester on a new Class of 'I'heorems in elimination 

between Quadratic Functions 213 

Proceedings of the Royal Society 219 

Cambridge Philosophical Society 230 

On the Compounds of Iodine and Phosphorus, by M. B. Coren- 

winder 234 

Description of some new Minerals from Norway, bv M. P. H. 

Weibye '....' 234 

On the Hyposklerite of Arendal, by M. C. Rammelsberg .... 237 



On the existence of Iodine in Beet-root, by M. Lamy 237 

Electro-Magnetism as a Motive Power 238 

Meteorological Observations for July 1850 239 

^ 'I'able. 240 


Prof. W. Thomson's Remarks on the Forces experienced by 
inductively Magnetized Ferromagnetic or Diamagnetic Non- 
crystalline Substances 241 

Prof. Graham on the Diffusion of Liquids {continued) 254 

Mr. J. Cockle on Impossible Equations, on Impossible Quanti- 
ties, and on Tessarines 281 

Mr. Reuben Phillips on the Magnetism of Steam 283 

Mr. W. Spottiswoode on a Georaetincal Theorem 289 

Mr. J. Kyd on the Chemical Formula of the Nitroprussides . , 289 
Mr. W. J. M. Rankine on the Anomaly- Ruler ; an Instrument 
to assist in the graphic representation of the place of a Gra- 
vitating Projectile in an Elliptic Orbit 291 

The Rev. T. P. Kirkman on Bisignal Univalent Imaginaries . . 292 
Notices respecting New Books : — Mr. J. K. Smythies's Essay 

on the Theory of Attraction 301 

Proceedings of the Royal Society 302 

Tenacity of Metals, by M. Baudrimont 308 

On the Artificial Formation of Lactic Acid and Alanin, by M. A. 

Strecker 308 

On the Action of Bases upon Salts, by M. Alvaro Reynoso . . 310 
New Demonstration of a Geometrical Theorem, by John Hen- 

nessy, jun.. Esq 312 

New mode of preparing Ethyalmin. Ethamic Acid 312 

On the Action of Carbon on Metallic Solutions, by M. Esprit. . 313 

On the Copper Test for Sugar, by M. Lassaigne 314 

New Reagent for Oxide of Carbon 315 

On a Cause of Variation in the Angles of Crystals, by M. J. 

Nickles ,' 316 

On the Extraction of Iodine from Plants and from Coal, by M. 

Bussy 317 

Bromine a product of the Distillation of Coal, by M. Mene . . 317 
Decomposition of Metallic Acids by Iodide of Potassium, by M. 

Schdnbein 318 

Note by M. Du Bois-Reymond on M. Matteucci's Paper on Elec- 
tro-Physiology 318 

Meteorological Observations for August 1850 319 

Table 320 



Mr. H. L. Ellis's Remarks on an alleged i)roof of the "Method of 
Least Squares," contained in a late Number of the Edinburgh 
Review. In a Letter addressed to Professor J. D. Forbes.. 321 
Mr. P. Clare's Account of some Thunder-storms and extra- 
ordinary Electrical Pha?nomena that occurred in the neigh- 
bourhood of Manchester on Tuesday the IGth of July 1850. 

(With a Plate.) 329 

Mr. J. K. Smythies's Essay on the Theory of Attraction .... 340 

Prof. Graham on the Diffusion of Liquids {cancluded) 341 

Mr. H. J. Brooke on the Crystalline Form of Beudantite .... 341) 

Prof. Williamson's Theory of ^Etherification 350 

Prof. Forbcs's Account of a remarkable Meteor, seen Dec. 19, 

1849 357 

Mr. J. J. Sylvester on a new Class of Theorems, and on Pas- 
cal's ITieorera. 363 

Mr. J. .T. Sylvester on the solution of a System of Equations in 
which three Homogeneous Quadratic Functions of three un- 
known quantities are respectively equaled to numerical Mul- 
tiples of a fourth Non-Homogeneous Function of the same. . 370 
Mr. J. Glaisher on the Meteorology of England and the South 

of Scotland during the Quarter ending September 30, 1850. . 373 
Prof. Thomson on a remarkable property of Steam connected 

with the Theory of the Steam-Engine 386 

Mr. J. Napier on the Conductibility of the Earth for Electricity 390 
Notices respecting New Books : — Mr. T. Tate on the Strength 

of Materials 391 

On the Minerals of the Auriferous Districts of Wicklow, by Wil- 
liam Mallet, Esq 392 

On Pyroglycerin, by M. Sobrero 394 

Preparation of Sulphurous Acid, by M. Boutigny 394 

On the Alteration which Well-water undergoes, by M. Blondeau 395 
On Emery, and the Minerals associated with it, by M. J. Lau- 
rence Smith 396 

On the Identity of the Equisetic, Aconitic and Citridic Acids, 

and on some Aconitates, by M. Baup 397 

On the Production of Succinic Acid by Fermentation, by M. Des- 


Meteorological Observations for September 1850 399 

Table 400 



Prof. Forbes on the alleged evidence for a Physical Connexion 
between Stars forming Binary or Multiple Groups, deduced 
from the Doctrine of Chances 401 

Mr. W. H. Barlow's Description of a new Electrical Machine. . 428 


Mr. W. Ferguson's Notice of the occurrence of Chalk Flints and 

Greensand Fossils in Aberdeenshire 430 

Mr. J. J. Sylvester on a Porismatic Property of two Conies 

having with one another a contact of the Third Order .... 438 
Mr. J. J. Sylvester on the Rotation of a Rigid Body about a 

Fixed Point 440 

Prof. Chapman on the Identity of Breislakite and Augite .... 444 
Prof. Chapman's Note on the employment of Right Rhomboidal 

Prisms in Crystallography 446 

Mr. G. Walker on the Theory of a new species of Locomotive 

Vessel that will diminish the ordinary resistance of the Water 

to one-fortieth part of its retarding power in Vessels of the 

same burthen. (With a Plate.) 447 

Mr. E. Wilde on the Untenableness of the received Theory of 

Newton's Rings 45 1 

Mr. R. Ellis's Note to a former paper " On an alleged proof of 

the ' Method of Least Squares.' " 462 

Mr. G. KirchhofFona Deduction of Ohm's Laws, in connexion 

with the Theory of Electro-statics 463 

Proceedings of the Cambridge Philosophical Society 468 

The first idea of the Electric Telegraph 470 

On the Sulphuric and Nitric Compounds of Benzin and Naph- 

thalin, by J\L A. Laurent 471 

On the Distillation of Mercury by High Pressure Steam, by M. 

Violette 472 

On the presence of Succinic Acid in the Human Body, by M. 

W. Heintz 473 

On a new Compound of Sulphur, Chlorine and Oxygen, by M. 

E. Millon 474 

Preparation and Analysis of Codeia, by Dr. Anderson 475 

On Hypochlorous Acid and the Chlorides of Sulphur^ by M. E. 

Millon 476 

On the Discoloration of Silver by boiled Eggs, by M. Gobley. . 477 

On a Test for Protein Compounds, by M. E. Millon 478 

Meteorological Observations for October 1850 . 479 

■■ Table 480 


Dr. Stenhouse on Aloine, the Crystalline Cathartic Principle of 
Barbadoes Aloes , . 481 

Mr. J. Bryce on Striated and Polished Rocks and " Roches 
Moutonnees " in the Lake District of Westmoreland. (With 
a Plate.) , 486 

Mr. J. Cockle's Analysis of the Theory of Equations. Second 
and Concluding Part, hi a Letter to T. S. Davies, Esq. . . 493 

Mr. R. Phillips's Remarks on the Theory of Thunder-storms. . 510 


Mr. A. .'. Robertson on the Positive Wave of Translation. 

(With a Plate.) 512 

Dr. Hare on the E.xplosiveness of Nitre, with a view to elucidate 

its agency in the tremendous explosion of Julv 1845, in New 

York ' 525 

Preparation of Atropiaby means of Chloroform, by M. Rabourdin 542 
On the Composition of certain natural Organic Bases, by M. A. 

de Planta 543 

On Spots on the Sun, by Prof. Colla 545 

On the Chemical Equivalent of Iron, by M. E. Maumend .... 546 
Index 547 


I. Illustrative of Mr. P. Clare's Paper on Thunder Storms and extraor- 
dinary Electrical Phaenomena. 

II. Illustrative of Mr. Bryce's Paper on Striated and Polished Rocks and 
"Roches Moutonnees " in the Lake District of Westmoreland. 

III. Illustrative of Mr. A.J.Robertson's Paper on the Positive Wave of 

IV. Illustrative nf Mr. G. Walker's Paper on the Theory of anew species 
of Locomotive Vessel, 






JULY 1850. 

I. Second Memoir on the Magneto-optic Properties of Crystals^ 
and the relation of Magnetism aiid Diamagnetism to Mo- 
lecular Arrangement. By John Tyndall and Hermann 

IN the year 1846 our views of magnetic action received, 
through tiie researches ot" Faraday, an extraordinary ex- 
pansion. The experiments of Brugmans, Le Baillif, Seebeck 
and Becquerel, had already proved tlie power to be active 
beyond the limits usually assigned to it; but these experi- 
ments were isolated, and limited in number. Faraday was 
the first to establish the broad fact, that there is no known 
body indifferent to magnetic influence, when the latter is 
strongly developed. The nature of magneiic action was then 
found to be twofold, attractive and repulsive; thus dividing 
bodies into two great classes, which are respectively denomi- 
nated magnetic and diamagnetic. 

The representative of the former class is iron, which, being 
brought before the single pole of a magnet, is attracted ; the 
representative of the latter class is bismuth, which, being 
brought before the single pole of a magnet, is repelled. 

If a little bar of iron be hung freely between the two poles 
of a magnet, it will set its longest dimension in the line joining 
the poles; a little bar of bismuth, on the contrary, will set its 
longest dimension at right angles to the line joining the poles. 

The position of the iron is termed by Mr. Faraday the 
axial', the position of the bismuth, the equatorial. We shall 
have occasion to use these terms. 

These discoveries, opening, as they did, a new field in phy- 
sical science, invited the labours of scientific men on the con- 
tinent. Weber, ffirsted, Reich and others, have occupied 
* Communicated by the Authors, 

Phil Mag, S. 3. Vol. 37. No, 24-7. July 1850. B 

2 Messrs. J. Tyndall and II. Knoblauch on the 

themselves with the suhject. But, if we except the illustrious 
discoverer himself, there is no investigator in this branch of 
science whose labours have been, to all appearance, so richly 
rewarded as those of Professor Pliicker ot Bonn. 

In 181-7 M. Pliicker had a magnet constructed of the same 
size and power as that described by Mr. Faratlay'-', iiis object 
being to investigate the influence of the fibrous constitution 
of plants upon their magnetic deportment. While conducting 
these experiments, he was induced to try whether crystalline 
structure exercised an influence. "The first experiment," 
says M. Pliicker, "gave an innnediate and decided reply." 

Following up his investigations with crystals, he was led to 
the affirmation of the following two laws: — 

" IVhen any crystal v:hatcver "with one optical axis is hrouglit 
betvcee?! the poles of a magnet^ the axis is repelled by each of the 
jwlcs ; and if the crystal possess two axes, each of these is rc- 
pelled, with the same force, by the two pioles. 

" The force which causes this repulsion is independent of the 
magnetism or diamagnetism of the mass of the crystal ; it de- 
creases with the distance more slowly than the magnetic infuence 
exerted by the polesf." 

It is perhaps worth explaining, that if, on exciting the mag- 
net, the optical axis take up the axial position, it is said to 
be attracted; if the equatorial, it is said to be repelled. 

The first experiment of M. Pliicker, which led to tiie affir- 
mation of these laws, was made with tourmaline. A jilate of 
the crystal which hatl been prepared for the purposes of po- 
Larization, twelve millimetres long, nine wide, and three thick, 
was suspended by a strong fibre between the poles of an 
electro-magnet. On sending a current round the latter, tiie 
plate, which was magnetic, set itself as an ordinary magnetic 
substance would do, with its longest ilimension from pole to 
pole. The optical axis of the crystal, thus suspended, was 

On han<£in<T the crystal, however, with its ontical axis hori- 
zontal; when the magnet was excited, the plate stood no longer 
as a. magnetic substance, but as a diamagnetic; its longest 
dimension being at right angles to the line joining the poles. 
The optical axis of the crystal was found to coincide with its 
length, and the peculiar deportment was considered as a proof 
thai the optical axis was repelled. 

This law was further established by experiments with Ice- 
land spar, (juartz. zircon, beryl, &c., and, as above stated, 
included crystals of all kinds, both optic positive and negative. 

* Pfiil. Mag., vol. xxviii. p. 396. 

t Poggendorff's Jmialen, vol. Ixxii. p. 75. 

Magneto-optic Properties of Crystals, 3 

It has, however, hitely iinderf)one consiilerable modification 
at llie hands of M. PUicker himself. In a letter to Mr. Fa- 
raday, which appears in page 4'50, vol, xxxiv. of this Maga- 
zine, he expresses himself as follows: — 

"The first and general law I deduced from my last expe- 
riments is the following one : — ' There will be either repulsion 
or attraction of the optic axes by the poles of a magnet, ac- 
cording to the crystalline structure of the crystal. If the 
crystal is a negative one, there will be repulsion; if it is expo- 
sitive one, there will be at traction'^ y^ 

This law applies to crystals possessing two optical axes, 
each of the saitl axes being attracted or repelled according as 
the crystal is positive or negative. It will simplify the subject 
if we regard the line bisecting the acute angle inclosed by the 
two axes as the resultant of attraction or repulsion ; for the 
sake of convenience, we shall call this the middle line. In 
positive crystals, therefore, the middle line, according to the 
above law, must stand axial; in negative crystals, equa- 
torial. It is also evident, that the plane passing through the 
optical axes must, in the one class of crystals, stand from pole 
to pole, in the other class at right angles to the line joining 
the poles. 

In explaining this new modification of the law, M. Pliicker 
lays particular emphasis upon the fact, that the attraction or 
repulsion is the result of an independent force, connected in 
no wav with the maonetism or diamasnetism of the mass of 
the crystal ; and this view is shared by Mr. Faraday, who, in 
expressing his concurrence with M. Pliicker, denominates the 
force in question an " optic axis force t-" 

The experiments described in our first paper upon this 
subject J, furnish, we conceive, sufficient ground of dissent from 
these views. In the case of five crystals of pure carbonate of 
lime (Iceland spar), we found the law of Pliicker strictly veri- 
fied, all five crystals being diamagnetic; on replacing, how- 
ever, a portion of the carbonate of lime by carbonate of iron, 
nature herself being the chemist in this case, the crystal was 
no longer diamagnetic, but magnetic; in every other respect 
it was physically unchanged ; its optical properties remained 
precisely as before, the crystal of carbonate of lime and the 
crystal of carbonate of lime ami iron being both negative. In 
the one case, however, the optical axis was attracted ; in the 
other, the said axis was repelled ; the attraction being evi- 
dently caused by the passage of the crystal from the diamag- 
netic into the magnetic state. 

* Phil. Mag., vol. xxxiv. p. 450. f Phil. Trans. 1849, p. 32. 

+ Phil. Mag.jvol. xxxvi. p. 178. 


4 Messrs. .!. Tyiulall and 11. Knoblauch on the 

We have examined other crystals of the same form as Ice- 
land spar, both mairnetic and dianiagnetic. In all cases, the 
former act in a manner jirecisely similar to the magnetic cry- 
stal already described, while the latter behave as the diamag- 
netic. The following are examples. 

Nitrate of Soda. — This crystal is exactly of the same form 
as carbonate of lime, and, like it, diamagnetic. Its deport- 
ment is in every respect the same. A rhombus cloven from 
the crystal and susjiended horizontally between the poles, sets 
its longer diagonal axial. Suspending the full crystal between 
the poles, with its optical axis horizontal, on exciting the mag- 
net this axis sets itself ecjuatorial. 

Bre.unnerile. — This is a crystal composed principally of 
carbonate of lime and carbonate of magnesia, but containing 
a sufficient quantity of the carbonate of iron to render it mag- 
netic. Suspended in the magnetic field, the optical axis stands 
from pole to pole. 

Doloinitc. — In this crystal a portion of the lime is replaced 
by protoxide of iron and protoxide of manganese, which in- 
gredients render it magnetic. The optical axis stands from 
pole to pole. 

Carbonate of Iron. — In the cases cited, the substitution of 
iron for calcium was paitial ; in the case before us it is com- 
plete. This crystal differs in nothing, save in the energy of 
its action, from the n)agnetic crystals already described. If 
a full crystal be hung between the poles, with its optical axis 
liorizontal, on closing the circuit and sending a current round 
the magnet, the saiil axis turns strongly into the axial line, 
vibrates through it quickly for a time, and finally comes to 
rest there. If a thin rhombus be cloven from the crystal and 
suspended from one of its obtuse angles with its parallel faces 
vertical, it will set itself exactly equatorial. In this case it 
is easy to see that the liorizontal projection of the optical 
axis, which passes through the obtuse angle of the crystal, 
stands axial. Hung from its acute angle, the rhombus takes 
up an oblique position, making a constant angle with the line 
joining the poles. To this position, if forcibly removed from 
it, it will invariably return. The position maybe either right 
or left of the axial line; but the angle of obliquity is always 
the same, being the angle which the optical axis makes with 
the face of the rhombus. Hung from the obtuse angle the 
obliquity is nothing — from the acute angle it is a maximum; 
the rhombus is capable of all degrees of obliquity between 
these extremes, the optical axis in all cases standi?ig exactly/ 
from pole to pole. 

Oxide of Iron, — The above phaenomena are exhibited even 

Magneto-optic Properties of Crystals. 3 

in a more striking manner by this crystal. So strong i< the 
directive power, that a rhombus, suspended from one of its 
obtuse angles, will set itself strongly equatorial, though its 
length may be fifteen or twenty times its breadth. 

What is the conclusion to be drawn from these experi- 
ments? We have first of all a diamagnetic crystal of pure 
carbonate of lime, which sets its optical axis equatorial. On 
substituting for a portion of the lime a quantity of protoxide 
of iron sufficient to render the crystal weakly magnetic, we 
find the position of the axis at once reversed. Replacing a 
still further quantity of the diamagnetic lime by a magnetic 
constituent, we find the action stronger, the force with which 
the optical axis takes up the axial }iosition increasing as the 
magnetic constituents increase. These experiments appear 
to be irreconcilable with the statement, that the position of the 
optical axis is independent of the magnetism or diamagnetism 
of the mass. 

Turning now to crystals possessing two optical axes, we 
find the law of Pliicker ecpially untenable; a forcible contra- 
diction is exhibited in the case of — 

DicJiroite. — This crystal, as is well known, receives its name 
from its ability to transmit light of different colours. The 
specimen examined by us is a cube. In the direction of the 
crystallographic axis, which coincides with the middle linc^ 
the light transmitted is yellowish; through the oilier four 
sides of the cube it is a deep blue. Suspended with the middle 
line iiorizontal, whatever be the position of that line before 
closing the circuit, the instant the magnetic force is developed 
it turns with surprising energy into the axial position and 
becomes fixed there. According to the law, however, the 
middle line shoidd stand equatorial, forthe crystal is negative-''. 

Sulphate of Barytes [heavy spar). — The form of this crystal 
is a prism whose base is a rhombus, the four sides being per- 
pendicular to the base. It cleaves parallel to the sides and 
base. Suspended between the poles, with the axis of the 
prism vertical, on exciting the magnet, the long diagonal sets 
itself axial. The crystal is diamagnetic, and agrees, thus fai-, 
with the carbonate of lime. Suspended fron? the acute angle 
formed by two hides of the }irism, the axis of the latter being 
horizontal, on closing the circuit the said axis turns into the 
axial position, and remains there as long as the force is pre- 
sent. Suspending the crystal from its obtuse angle, the axis 
being still horizontal, on closing the circuit the axis sets itself 
equatorial. A plane perpendicular to the rhombic base, and 
passing through the long diagonal, contains the two optical 
* Brewster's list. 

6 Messrs. J. Tyndall and H. Knoblauch on the 

axes, wliich are inclined to each other at an angle of SS'^. 
The middle line bisecting this angle is parallel to the axis of 
the prism, and hence stands axial or vqiiatorial^ according as 
the prism is suspended from its acute or its obtuse angle. 
The position of the middle line is therefore a function of the 
point of suspension, varying as it varies ; at one time support- 
ing the law of Pliicker, and at another time contradicting it. 
Heavy spar is positive. 

Sulphate of Strnntia (Ccelestine). — 'J'his is also a jiositive 
crystal, its form being precisely that of heavy spar ; the only 
dift'erence is, that, in the case before us, the optic axes inclose 
an angle of 50^ instead of 38^. The corroboration and con- 
tradiction of heavy spar are exhibited here also. 

Sulphate of%inc. — Suspend the crystalline prism from its 
end, and mark the line which stands equatorial when the mag- 
net is excited. A plate taken from the crystal parallel to this 
line, and to the axis of the prism, on examination widi polar- 
ized light, will display the ring systems surrounding the ends 
of the two optic axes. The middle line, therefore, which bi- 
sects the acute angle inclosed by these, stands axial. It ought, 
however, to stand equatorial, for the crystal is negative. 

Sulphate of Magnesia. — Suspending the crystalline prism 
from its end, and ibllowing the method ajiplied in the case of 
sulphate of zinc, we discover the ring systems and the position 
of the middle line. This line stands axial, but the crystal is 

Topaz. — Thii' being one of the crystals pronounced by M. 
Pliicker as peculiarly suited to the illustration of his new law, 
it is perhaps on that account deserving of more than ordinary 
attention. In the letter to Mr. Faraday, before alluded to, 
M. Pliicker writes : — 

"The crystals most fitted to give the evidence of this law 
are diopside (a positive crystal), crjanite^ topaz (both negative), 
and others crystallizing in a similar way. In these crystals 
the line (A) bisecting the acute angles made by the two 
optic axes, is neither perpendicular nor parallel to the axis 
(B) of the prism. Such a prism, suspended horizontally, will 
point neither axially nor equatorially, but will take always a 
fixed intermediate direction. This direction will continually 
change if the prism be turned round its own axis (B). It may 
be proved by a simple geometrical construction, which shows 
that during one revolution of the prism round its axis (B), 
this axis, without passing out of two fixed limits C and D, 
will go through all intermediate positions. The directions C 
and D, where the crystal returns, make, either with the line 
joining the two poles, or with the line perpendicular to it, on 

Magnet O'Optic Properties of Crystals. 7 

both sides of these lines, angles equal to the angle included by 
A and B; tlie first being the case if the crystal be a positive 
one, the last if a negative one. Thence it follows, that if the 
crystal, by any kind of horizontal suspension, should point to 
the poles of a magnet, it is a positive one; if it should point 
equatorial ly, it is a negative one*." 

In experimenting with this crystal, we have found the great- 
est care to be necessary. Its dianiagnetic force is so weak, 
that the slightest local impurity, contracted by handling or 
otherwise, is sufficient to derange its action. The crystals as 
they come from the mineralogist are unfit for exact experi- 
ment. We have found it necessary to boil those which we 
have used in muriatic acid, and to scour them afterwards with 
fine white sand, reduced to powder in a mortar. These pre- 
cautions taken, we have been unable to obtain the results de- 
scribed by M. Pliicker. We have examined five specimens 
of topaz from Saxony, the axial dimension of some of them 
exceeding the dimension perpendicular thereto by one-half;- 
the axis, notwithstanding, stands in all cases from pole to pole. 
Two specimens of Brazilian topaz, the one of an amber colour, 
the other almost as clear as distilled water,- give the same re- 
sults ; the axes of the crystals stand from pole to pole, and 
turning round makes no difference. On a first examination, 
some of the crystals exhibited an action similar to that de- 
scribed by M. Pliicker ; after boiling and scouring, these 
irregularities disappeared, and they one and all stood axial. 

One crystal in particular caused us considerable embarrass- 
ment. Its action was irregular, and the irregularity remained 
after the adoption of the methods described to ensure purity. 
A splinter from one of its sides was found to be attracted, 
a splinter from the side opposite was found to be repelled. 
To the naked eye the crystal appeared clean and clear. On 
examination, however, under a powerful microscope, the side 
of the crystal from which the nnignetic splinter was taken was 
found dotted with small black particles imbedded in its mass; 
the other side of the crystal was perfectly transparent. On 
cleaving away the impurities, the irregularity vanished, and 
the crystal stood as the others. 

In the letter (juoted, dioj)side is j)ronounced by M. Pliicker 
to be a positive crystal. On examination with circular polar- 
ized light, as recommended by Dovef, we find the crystal to 
be negative. The same method pronounces topaz positive, 
instead of negative, as affirmed by M. Pliicker. The speci- 
mens we have examined in this way are from Brazil and 

* Phil. Mag.,voU xxxiv. p. 450. 

t Poggendorff's Annalan, vol. xl. pp. 457, 482. 

S Messrs. J. Tyndall and H. Knoblauch on the 

Saxony. Aberdeen topaz \vc liave not examined, but it also 
is classed by Brewster anionii; positive crystals. Tlie obli- 
quity of the middle line of to})az does not exist in the speci- 
mens which have come under our notice ; it is exactly per- 
pendicular to the principal cleavage, and consequently exactly 
parallel to the axis of the prism. This agrees vvith the results 
of Brew.ster, who found the optical axes to be "equally in- 
clined to the plane of cleavage*." 

In experimenting witli weak diamagneticcrystals, the greater 
the number of examjiles the better; as, if local impurity be 
present, it is thus more liable to detection. Our results with 
lieavy spar liave been confirmed by ten different crystals ; with 
coelestinc, by five; and with topaz, as has been stated, by seven. 
The suspending fibre, in these and similar instances, was a 
foot loni; and -4—, of an inch thick, or about oiie-eijrhth of the 
diameter of a human hair. 

Sugar. — It is well known that this crystal forms a prism 
with six sides, two of which are generally very prominent, the 
principal cleavage being parallel to these two, and to the 
wedge-like edge which runs along the end of the prism. The 
plane of ihe optical axes is perpendicular to the axis of the 
prism, and their ends may be found by cutting out a plate 
jiarallel to that axis, and inclined to the principal cleavage at 
an angle of about '2.0°. Such a plate exhibits both ring 
systems symmetrically, while a plate parallel to the principal 
cleavage exhibits one system only. Suspended between the 
excited poles, with the axis of the prism horizontal, and the 
principal cleavage vertical, the plane of the optical axis stands 
axial; according to the law of M. Pliicker, it ought to stand 
equatorial, for the crystal is negative. 

Rock-crystal {Quartz). — This crystal has undei'gone more 
than one examination by M. Pliicker, its deportment being, 
"contrary to all expectation," very weak — a result, it maybe 
remarked, difficult of explanation on the hypothesis of an 
" optic axis force." M. Pliicker's first experiments with this 
crystal were apparently made with great exactitude, the cry- 
stal being reduced to a spherical shape, and the influence of 
mere form thus annulled. These experiments proved the 
optical axis to be repelled. Later researches, however, in- 
duced this philosopher to alter his opinion, and accordingly, 
in his last memoirf, we find quartz ranked with those crystals 
whose optical axes are attracted, with the remark " weak " 
added parenthetically. We have not been able to obtain this 

* Lardnei's Encjclopaedia, Optics, p. 204. 
f Poggendorl!''s Annalen, vol. Ixxviii. p. 4''28. 

Magneto-optic Properties of Crystals. 9 

deportment. After the washing and scouring process, the 
finest and most transparent crystals we could procure con- 
firmed the first experiments of M. Pliicker, and therefore 
contradict the new modification of his hiw. It is ahiiost in- 
credible how slight an impurity is suilicient to disturb the 
action of this crystal. A specimen with smaller crystals at- 
tached to it, or growing through it, is suspicious and ought 
to be rejected. Clear isolated crystals are alone suitable. 
We must remark that a fine cube, with i^aces half an inch 
square, suspended with the optic axis iiorizontal, showed no 
directive action ; either one or the other of the diagonals set 
itself from pole to pole, though the axis ran parallel to four of 
the faces. 

As far as it has been practicable, we have cut and cloven, 
and examined the optical properties of the crystals which have 
passed through our hands ourselves, testing, in every possible 
case, the results of others by actual experiment. Most of the 
crystals in Brewster's list have been gone through in this 
way. Iceland spar, quartz, mica, arragonite, diopside, lepi- 
dolite, topaz, saltpetre, sugar, sulphate of zinc, sulphate of 
magnesia, and others have been examined and verified. In 
two cases, however, our results differed from the list, these 
being sulphate of nickel and borax. A prism of sulphate of 
nickel was suspended from its end between the poles ; on ex- 
citing the magnet it took up a ileterminate position. When 
it came to rest, a line parallel to the magnetic axis was 
marked thereon, and a plate taken from the crystal parallel to 
this line and to the axis of the prism. Such a plate, ground 
thin, exhibited in the polariscope a pair of very beautiful 
ring systems. The ring systems of borax were found in a 
similar manner. The middle line, therefore, in both cases 
stood equatorial, and, according to the list, would contradict 
the law of M. Pliicker, for both are there set down as. positive. 
A careful examination with circular polarized light led us to 
the opposite conclusion. We thought it worth while to send 
specimens of each to Berlin, so as to have them examined by 
Professor Dove, the author of the method by which we ex- 
amined them. The crystals have been returned to us with 
a note certifying that they are negative, and thus confirm- 
ing our observations. This certificate has reached us in the 
form of a private note, but we believe Professor Dove will 
not charge us widi imprudence for thus availing ourselves of 
such a high authority as his opinion confessedly is in optical 

Yelloio Ferrocyaiiide of Potassium. — This crystal does not 
stand in the list of Brewster, and we have sought for it in 

10 Messrs. J. Tviulall and II. Knoblauch on the 

other lists in vain. In one German work on physics wo find 
Blutlaugcnsah set clown as a ne<;ative crystal with one optical 
axis, but whether the red or yellow salt is meant, the author 
does not explain. We have examined the crystal ourselves, 
and find it positive with two optic axes. The middle line 
stands perpendicular to tiie principal cleavage. Suspended 
with this line horizontal, on closing the circuit it sets itself 
equatorial. Another exception to the law under considera- 
tion is here exhibited. 

M. Pliicker recommends the magnet as a practical means 
of determinino- whether a crystal is positive or negative; this 
method being attended with the peculiar advantage that it 
can be a|)plied in the case of opake crystals, where all the 
ordinary methods fail. We find accordingly, in his last me- 
moir on this subject, metallic and other opake crystals with 
optical properties attributed to them. Antimony is negative 
witii one optic axis; bismuth and arsenic are positive with 
one o}itic axis. The foregoing experiments demonstrate the 
insecurity of the basis on which this classification rests. 

By looking back upon the results described, it will be seen 
that we have drawn from each respective class of crystals one 
or more examples which disobey the law of M. Pliicker. Of 
positive crystals with one axis, we have quartz; of positive 
crystals wiUi two axes, we have heavy spar, ccelestine and 
ferrocyanide of potassium. Of negative crystals with one 
axis, we have carbonate of lime and iron, and several others; 
of negative crystals with two axes, we have dichroite, sugar, 
sulphate of zinc, and sulphate of magnesia. It is due how- 
ever to jSI. Pliicker to state, that in a considerable number of 
cases we have found the law confirmed. Tourmaline, idocrase, 
beryl, Iceland spar, saltpetre, arragonite, and many others all 
confirm it. Singularly enough, these are the very crystals 
with which M. Pliicker has experimented. It is therefore 
not to be wondered at, that he should be led by such a mass 
of concurring evidence to pronounce his law general. Had 
his experiments embraced a sufficient number of cases, they 
would doubtless have led him to the same conclusion to which 
ours have conducted. 

Mr. Faraday has devoted considerable time to the investi- 
gation of this intricate subject. His most notable experi- 
ments are those with bismuth, nntimom/, arsenic, sulphate of 
iron, and sulphate of nickel, which experiments we have care- 
fully repeated. 

Bisimith. — Crystals of bismuth we have ourselves prepared, 
by melting the metal in a Hessian crucible, placed within a 
larger one and surrounded by fine sand. In this state it was 

Magneto-optic Properties of Crystals. 1 1 

allowed to cool slowly, until a thin crust gathered on the sur- 
face. At this point the crust was pierced, and the molten 
metal underneath poured out, thus leavin^r the complete cry- 
stals clustering round the sides and bottom. Our experi- 
ments with these crystals corroborate, to tlie letter, those so 
minutely described by Mr. Faraday in the Bakerian Lecture 
for J849, delivereil before the Royal Society*. 

ylrscnic. — Our arsenic we obtained at the druggists. It is 
well known that this metal is usually obtained by the sublima- 
tion of its ore, the vapour being condensed in suitable re- 
ceivers, where it is deposited in a crystalline form. There is 
a difference of opinion between INIr. Faraday and M. PKicker 
as regards this metal; the former holding it for diamagnetic, 
the latter for magnetic. Several specimens, obtaineil from 
different druggists, corroborated the view of M. Pliicker. 
They were all magnetic. 

About half an ounce of the metal was introduced into a 
glass tube closed at one end and open at the other. About 
five inches of the tube, near the open end, was crammed full 
of copper turnings, and the open end introduced through a 
small aperture into the strong draft of a flue from a heated 
oven. The portion of the tube containing the copper turn- 
ings was heated to redness, and by degrees the oxygen within 
the tube was absorbed. The arsenic at the other eiid was 
then heated and sublimed. After some time the vapour was 
allowed to condense slowly, and a metallic deposit was the 
consequence — the arsenic thus obtained was diamagnetic. 
The deportment of the crystal is described by Mr. Faraday 
in the place referred to. 

Antimony. — A difference of opinion exists with regard to 
the action of this crystal also. Referring to the deportment 
assigned to it by Mr. Faraday, M. Pliicker writes, "to my 
astonishment however antimony behaved in a manner directly 
the reverse. While on the one side a prism of bismuth, 
whose principal cleavage coincided with the base of the prism, 
set itself axial; and on the other side a plate of arsenic, 
which, on account of its magnetism, ought to stand axial, set 
'MfiftM equatorial ; a plate of antimony deviated completely from 
this deportment, and although the mass was strongly dia- 
magnetic, set itself decidedly axialT 

INI. Pliicker's results differ from those of Mr. Faraday in 
two particulars; first, a plate of antimony, similar to that de- 
scribeil by M. Pliicker, is found by Mr. Faraday to stand 
equatorial instead o^ axial \ second, the following phaenomena, 
observed by Mr. Faraday, appear not to have exhibited 
* Pliilosopliical Transactions. 1849, p. 1. 

12 Messrs. J. Tviulall and IJ. Knoblauch on the 

tliemselves in M. Pliicker's experiments: — "On the develop- 
ment of the magnetic force, the crystal went np to its position 
slowly, and pointed as with a ilead set. Other crystals diti 
the same imjiertectly ; and others again made one or perhaps 
two vibrations, but all aj)peared as if they were moving in a 
thick fluid, and were, in that respect, utterly unlike bismuth, 
in the freedom and mobility with which it vibrated. If the 
crystalline mass was revolving when the magnetic force was 
excited, it suddenly stopped, and was caught in a position 
which might, as was found by experience, be any position. 
The arrest was followed by a revulsive action on the discon- 
tinuance of the electric current*." 

In most of the specimens examined by us these phaenomena 
were also absent, and the results of M. PRicker presented 
themselves. Three sjiecimens however behaved exactly in 
the manner described by Mr. Faraday, exhibiting a singular 
inertness when the magnetic force was present, and a revul- 
sion from the poles on breaking the circuit. To ascertain, if 
possible, the cause of this difference, we dissolved an example 
of each class in muriatic acid, precipitated the antimony with 
distilled water, and tested the clear filtrate with ferrocyanide 
of potassium. The specimen which agreed with M. Pliicker 
exhibited a faint bluish tint, characteristic of the presence of 
iron ; that which corroborated Mr. Faraday showed not the 
slightest trace of this metal. The iron, though thus revealing 
itself, must have been present in a cjuantity exceedingly mi- 
nute, for the antimony was diamagnetic. Whether this has 
been the cause of the difference between M. Pliicker and Mr. 
Faraday we will not undertake to say; irregular crystalline 
structure may also have had an influence. 

We have here a crowd of examples of crystalline action 
in the magnetic field, but as yet not a word of explanation. 
M. Pliicker's hypothesis has evidently failed. We now turn 
to liie observations of Mr. Faraday, and shall endeavour to 
exhibit, in the briefest manner possible, the views of this pro- 
found investigator. 

After a general description of the action of bismuth between 
the poles, Mr. Faraday writes : — " The results are, altogether, 
very different from those produced by diamagnetic action. 
They are equally distinct from those dependent on ordinary 
magnetic action. They are also distinct from those discovered 
and described by Pliicker, in his beautiful researches into the 
relation of the optic axis to magnetic action ; for there the 
force is equatorial, whereas here it is axial. So they appear 

* Philosophical Transactions, 1849, p. 14. For an explanation see Plii- 
losophical Magazine, vol. xxviii. p. 460. 

MngnetO' optic Properties nf Crystals. 13 

to present to us a new force, or a new form of force in the 
molecules of matter, which for convenience sake, I will con- 
ventionally designate by a new word, as the ma gn eery stall ic 

'•The magnecrystalllc force appears to be very clearly 
distinguished from either the matjiietic or diamagnetic forces, 
in that it causes neither approach nor recession ; consisting 
not in attraction or repulsion, but in its giving a certain de- 
terminate position to the mass under its influence, so that a 
given line in relation to the mass is brought by it into a given 
relation with the direction of the external magnetic powerf." 

The line through the crystal which sets itself with greatest 
force from pole to pole, is termed by Mr. Faraday the magne- 
crystallic axis of the crystal. He proves by experiment that 
bismuth has exactly the same amount of repulsion whether 
this axis be parallel or transverse to the lines of magnetic force 
acting on it. 

" In other experiments a vertical axis was constructed of 
cocoon silk, and the body to be examined was attached to it 
at right angles as radius ; a prismatic crystal of sulphate of 
iron, for instance, whose length was four times its breadth, 
was fixed on the axis with its length as radius and its magne- 
crystallic axis horizontal, and therefore as tangent ; then, when 
this crystal was at rest under the torsion force of the silken 
axis, an electro-magnetic pole was so placed that the axial 
line of magnetic force should be, when exerted, oblique to 
both the length and the magnecrystallic axis of the crystal ; 
and the consequence v/as, that, when the electric current cir- 
culated round the magnet, the crystal actually receded from 
the magnet under the influence of the force, which tended to 
place the magnecrystallic axis and the magnetic axis parallel. 
Employing a crystal or plate of bismuth, that body could be 
made to approach the magnetic pole under the influence of 
the magnecrystallic force; and this force is so strong as to 
counteract either the tendency of the magnetic body to ap- 
proach or of the diamagnetic body to retreat, when it is ex- 
erted in the contrary direction. Hence Mr. Faraday con- 
cludes that it is neither attraction nor repulsion which causes 
the set or determines the final position of a magnecrystallic 
body J." 

" As made manifest by the phsenomena, the magnecrystallic 
force is a force acting at a distance, for the crystal is moved 
by the magnet at a distance, and the crystal can also move 
the magnet at a distance." Mr. Faraday obtained the latter 
result by converting a steel bodkin into a magnet, and suspend- 

• Phil. Trans., 1849, p. 4. f Phil, Trans,, 1849; p. 2^. 

X Phil. Mag. vol, xxxiv, p. 77. 

14- ]\Iessvs. J. Tviulnll (Dui II. Knoblauch on the 

\Ui^ it fVoely in the neiiflibouihoocl of the crystal. The ten- 
dency of" the needle was always to jilace itself parallel to the 
ina«jnecryslallic axis. 

Crystals of bismuth lost their power of pointinjj^ at the mo- 
ment the metal be^an to fuse into drops over a spirit-lamp or 
in an oil-bath. *' Crystals of antimony lost their ma^necry- 
stallic power below a dull red heat, and just as they were 
sofleiiinij; so as to take the impression of the copper loop in 
which thev were hung." Iceland spar and tourmaline, on 
the contrary, on being raised to the highest temperature which 
a spirit-lamp could give, underwent no diminution of force; 
they pointed equally well as before. 

Mr. Faraday finally divides the forces belonging to crystals 
hi to two — inherent and mduced. An example of the former 
is the force by wliich a crystal modifies a ray of light which 
passes through its mass; the second is developed exclusively 
by magnetic power. To this latter, as distinct from the other, 
Mr. Farada}- has given the name magnetocrystallic. To ac- 
count for crystalline action in the magnetic field, we have, 
therefore, the existence of three new forces assumed : — the 
optic axis force, the magnecrystallic force, and the magneto- 
crystallic force. 

U'ith regard to the experimental portion of Mr. Faraday's 
labours on this subject, we have only to express our admira- 
tion of the perfect exactitude with which the results are given. 
It ap'pears to us, however, a matter of exceeding difficulty to 
obtain a clear notion of any such force as he has described ; 
that is to say, a force proceeding fi'om the }iole of a magnet, 
and capable of producing such motions in the magnetic field, 
and yet neither attractive nor repulsive. 

That a crystal of bismuth should approach the magnetic 
pole, and that a crystal of sulphate of iron should recede 
therefrom, appears, at first sight, anomalous, but certainly 
not more so than other phsenoiiiena connected with one of 
Mr. Farada, 's most celebrated discoveries, and explained in 
a beautiful and satisfactory manner by himself. 

If we hang a penny from its edge in the magnetic field, and 
so arrange the suspending thread, that the coin, before the 
magnetic power is developed, shall make an angle of 45°, or 
thereabouts, with the line joining the poles ; then, on closing 
the circuit, aUvl sending a current round the mognet, the coin 
will suddenly turn, as if it made an effort to set itself from 
pole to pole ; and if its position beforehand be nearly axial, 
this effort will be sufficient to set it exaclhj ?.o', the penny 
thus behaving, to all appearance, as if it were attracted by 
the poles. 

The real cause of this however is repulsion. During the 

Magneto-optic Properties of Cri/xtals. 1 5 

development of inaonetic power, an electrie stream is aroused 
in the copjier coin, which circulates round the coin in a di- 
rection oj)[)osite to that oF the current wiiicli passes from the 
battery round the coils of the magnet. I'he efiect of this in- 
ducetl stream is to create a pohir axis in the copper; and 
when tile direction of the stream is considereii, it is easy to 
see that the north end of this axis must face the north pole 
of the magnet, and will ct)nsequently be repelled. On looking 
therefore at the penny, apparently attracted as above de- 
scribed, we must, if we would conceive rightly of the matter, 
witlulraw our attention from the coin itself, and fix it on a 
line passing throngh its centre, and at right angles to its flat 
surface; this is the polar axis of the penny, the repulsion of 
which causes the apparent attraction. 

We do not mean to say that any such action as that here 
described takes place with a bismuth crystal in the magnetic 
field. The case is cited merely to show tliat the "approach " 
of the bismuth crystal, noticed by Mr. Faraday, wzaz/, be really 
due to repiilsio7i ; and the "recession " of the sulphate of iron 
really due to attraction. 

Our meaning will perhaps unfold itself more clearly as we 
proceed. If we take a slice of apple, about the same size as 
the penny, but somewhat thicker, and pierce it through with 
short bits of iron wire, in a direction perpendicular to its flat 
surface, such a disc, suspended in the magnetic field, will, on 
the evolution of the magnetic force, recede from the poles and 
set itself strongly equatorial ; not by repulsion, but by the 
attraction of the iron wires passing through it. If, instead of 
iron, we use bismuth wire, the disc, on exciting the magnet, 
will turn into the axial position ; 7iot by attraction, but by 
the repulsion of the bismuth wires passing through it. 

If we suppose the slice of apple to be replaced by a little 
cake made of a mixture of flour and iron filings, the bits of 
wire running through this will assert their predominance as 
before ; for though the whole is strongly magnetic, the supe- 
rior energy of action along the wire will detei'mine the position 
of the mass. If the bismuth wire, instead of piercing the 
apple, pierce a little cake made of flour and bismuth filings, 
the cake will stand between the poles as the apple stood ; for 
though the whole is diamagnetic, the stronger action along 
the wire will be the ruling agency as regards jiosition. 

Is it not possible to conceive an arrangement among the 
particles of a magnetic or diamagnetic body, capable of pro- 
ducing a visible result similar to that here (lescril)ed? If the 
magnetic and diamagnetic forces be associated with the par- 
ticles of matter, is it not a reasonable inference, that the closer 

IG Messrs. J. 'lyndall niid II. Knoblaucli on the 

these particles are aii^greoateil, the less will be the obstruction 
ofl'erecl to the transmission of the respective forces among 
them.'' It is this closeness of arrangement in the cases just 
citeJ, wliicli gives to the iron and bismuth wire their predomi- 
nance; for the interposetl flour jiarticles obstruct the forces in 
all other directions. M^ therefore, in a magnetic or diamagnetic 
mass, two directions exist, in one of which the contact of the 
particles is closer than in the otiier, may we not fairly con- 
clude that the strongest exhibition of force will be in the for- 
mer line, wiiicli therefore will signalize itself between the 
poles, in a manner similar to the bismuth or iron wire? The 
case seems analogous to that of good and bad conductors in 
electricity. This fluid will not quit the good conductor to go 
to the bad. The powder magazine is safe, because the fluid 
prefers the iron rod to any other path. As regards magnet- 
ism, different directions, through the same hodi/^ may represent 
these good and bad conductors; the Ihie of prejercnce being 
that of closest contact among the material particles. 

If analogic proof be of any value, we have it here of the very 
strongest description. For example : — bismuth is a brittle 
metal and can readily be reduced to a fine powder in a mor- 
tar. Let a teaspoonlul of the powdered metal be wetted with 
gnm-waler, kneaded into a paste, and made into a little roll, 
say an inch long and a quarter of an inch across. Hung be- 
tween the excited poles, it will set itself like a little bar of bis- 
muth—equatorial. Place the roll, protected by bits of paste- 
board, within the jaws of a vice, squeeze it flat, and suspend 
the plate thus formed between the poles. On exciting the 
magnet the plate will turn, with the energy of a magnetic sub- 
stance, into the axial position, though its length may be ten 
times its breadth. 

Pound a piece of carbonate of iron into a fine powder, and 
form it into a roll in the manner described. Hung between 
the excited poles, it will stand as an ordinary magnetic sub- 
stance — axial. Squeeze it in the vice and suspend it edge- 
ways, its position will be immediately reversed. On the de- 
velopment of the magnetic force, the plate thus formed will 
recoil fi'om the poles, as if violently repelled^ and take up the 
equatorial position. 

\\'e have here " approach " and " recession," but the cause 
is evident. The line of closest contact is perpendicular in each 
case to the surface of the plate — a consequence of the pressure 
which the particles have undergone in this direction ; and 
this perpendicular stands axial or equatorial according as the 
plate is magnetic or diamagnetic. We have here a " a direc- 
tive force/' but it is attraction or repulsion modified. May 

Magneto-optic properties of Crystals. 1 7 

not that which has been here effected by artificial means occur 
naturally ? Mitst it not actually occur in most instances? for, 
where perfect homogeneity of mass does not exist, there will 
always be a preference shown by the forces for some particular 
direction. This election of a certain line is therefore the rule 
and not the exception. It will assist both the reader and us 
if we give this line a name ; we therefore propose to call it 
the line of elective polarity. In magnetic bodies this line will 
stand axial, in diamagnetic equatorial. 

"The relation of the magnecrystallic force," says Mr. Fa- 
raday, " to the magnetic field is axial and not equatorial." 
This he considers to be proved by the following considera- 
tions : — suppose a crystal of bismuth so suspended that it sets 
with its maximum degree of force, then if the point of suspen- 
sion be moved 90° in the axial plane, so that the line which in 
the last case stood horizontal and axial, may now hang verti- 
cal, then the action is a minimum : now, contends Mr. Fara- 
day, if the force were equatorial this change in the axial plane 
ought not to have affected it; that is to say, if the force act 
at right angles to the axial plane, it is all the same which 
point of the plane is chosen as the point of suspension. 

This seems a fair conclusion ; but the other is just as fair 
— that, if the force be axial, a change of the point of suspen- 
sion in the equatorial plane cannot disturb it. Mr. Faraday 
finds the line of maximum force in sulphate of nickel to be 
parallel to the axis of the prism. Whatever, therefore, be 
the point of suspension in the plane perpendicular to the axis, 
the action ought to be the same. On examining this crystal 
it will probably be found that two opposite corners of the 
parallelopiped are a little flattened. Let the prism be hung 
with its axis horizontal and ihxs Jlatteniug vertical, and after 
the evolution of the magnetic force let the oscillations of the 
prism be counted. Move the point of suspension 90^ in the 
equatorial plane, so that the flattening shall be horizontal, and 
again count the oscillations,. The numbers expressing the 
oscillations in both cases will be very different. The former 
will be a maximum, the latter a minimum. But if the force 
be axial this is impossible, therefore the force is not axial. 

Whatever be the degree of conclusiveness which attaches 
itself to the reasoning of Mr. Faraday drawn from bismuth ; 
precisely the same degree attaches to the above drawn from 
sulphate of nickel. The conclusions are equal and opposite, 
and hence destroy each other. It will probably be found that 
the reasoning in both cases is entirely correct; that the force 
is neither axial nor equatorial, in the sense in which these 
terms are used. 

Phil, Mag. S. 3. Vol. 37. No. 247. My 1850. C 

18 Messrs. J. Tyndall and H. Knoblauch on the 

A number of tliin plates, each about half an inch square, 
were cut from ahnond kernels, with an ivory blade, parallel to 
the cleft which divides the kernel into two lobes. These were 
aid one upon the other, with an interval of stron<r gum be- 
tween, until a cube was obtainetl. A few minutes in the sun- 
shine sulHced to render the cube dry enough for experiment, 
llimg between the poles, with the line }ierpendicular to the 
layers horizontal, on exciting the magnet this line turned and 
set itself parallel to the magnetic resultant passing through 
the mass. The action liere was a mascinmm. Turning the 
cube round 90° in the axial plane, there was scarcely any di- 
rective action. If the word ' crystal ' be substituted for ' cube ' 
in the description of this deportment, every syllable of it is 
applicable to the case of bismuth; and if the deportment of 
the crystal warrant the conclusion that the force is axial, the 
deportment of the cube warrants the same conclusion. Is the 
force axial in the case of the cube? Is the position of the 
line perpendicular to its layers due to the •' tendency " of 
that line to set itself {parallel to the magnetic resultant? The 
kernel is strongly diamagnetic, and the position of the per- 
pendicular is evidently a secondary result, brought about by 
the repulsion of the layers. Is it not then possible, that the ap- 
proach of the magnecrystallic axis, ifi bismuth, to the magnetic 
resultant, is really (hie to the repulsion of the planes of clea- 
vage P 

But here the experiment with the silken axis meets us; 
which showed that so far from attraction being the cause of 
action in a magnetic crystal, there was actual recession ; and 
so far from repulsion being the cause in a diamagnetic crystal, 
there was actual approach. This objection it is our duty to 

A model was constructed of powdered carbonate of iron, 
about 0'3 of an inch long and O'l in thickness, and, by atten- 
tion to compression, it was arranged that the line of elective 
polarity through the model was perpendicular to its length. 
Suspending a thread of cocoon silk with a weight at one end 
a vertical axis was obtained ; a bit of card was then slit and 
fitted on to the axis, so that when the model was laid on one 
side, the card stood like a little horizontal table in the middle 
of the magnetic field. The length of the model extended irom 
the central axis to the edge of the card, so that when the 
mass swung round, its line of elective polarity was tangent to 
the circle described. 

When the model was made to stand between the flat-faced 
poles obliquely, the moment the magnet was excited it moved, 
tending to set its length equatorial and its line of elective 

Magneto-optic j^yopertics of Crijstals. 19 

polarity parallel to the lines of magnetic force. In this ex- 
periment therefore the model of carbonate of iron, though a 
magnetic body and strongly attracted by such a magnet as 
that used, actually receded from the magnet. 

If, instead of the model of carbonate of iron, we substitute 
a crystal of sulphate of iron, we have Mr. Faraday's experi- 
ment instituted to prove the absence of attraction or repulsion. 
The dimensions are his dimensions, the arrangement is his 
arrangement, and the deportment is the exact deportment 
which he has observed. We have copied his very words, 
these words being perfectly descriptive of the action of the 
model. If, then^ the experiment be "a striking proof that 
the effect is not due to attraction or repulsion" in the one 
case, it must also be such in the other case; but the able ori- 
ginator will, we imagine, hardly push liis principles so far. 
He will, we doubt not, be ready to admit, that it is more pro- 
bable that a line of elective polarity exists in the crystal, than 
that a magnecrystallic axis exists in the model*. 

By a similar proceeding, using bismuth powder instead of 
carbonate of iron, the action of Mr. Faraday's plate of bis- 
muth may be exactly imitated. The ohjection to the conclusioiiy 
that the approach of the magnecrystallic axis^ in bisrmith, to the 
magnetic resultant, is due to the repidsion of the planes of clea- 
vage, is thus, "die conceive, fairly met. 

Let us look a little further into the nature of this magne- 
crystalllic force, which, as is stated, is neither attraction nor 
repulsion, but gives position only. The magnecrystallic axis, 
says Mr. Faraday, tends to place itself parallel to the magnetic 
resultant passing through the crystal; and in the case of a 
bismuth plate, the recession from the pole and the taking up 
of the equatorial position is not due to repulsion, but to the 
etideavour the bismuth makes to establish the parallelism 
before-mentioned. Leaving attraction and repulsion out of 
the question, we find it extremely difficult to affix a consistent 
meaning to the words ' tends ' and ' endeavour.' " The force 
is due," says Mr. Faraday, "to that power of the particles 
which makes them cohere in regular order, and gives the mass 
its crystalline aggregation, which we call at times the attraction 
of aggregation, and so often speak of as acting at insensible 
distances." We are not sure that we fully grasp the meaning 
of the philosopher in the present instance; for the difficulty 
of supposing that what is here called the attraction of aggre- 
gation, considered apart from magnetic attraction or repulsion, 

* The term magnecrystallic axis may with propriety be retained, even 
should our views prove correct ; but then it must be regarded as a subde- 
nomination of the line of elective polarity. 


Co Messrs. J. Tynclall and II. Knoblauch on the 

can possibly caiii=,e the rotation of the entire mass round nn 
axis, and the takinj^ up of a fixed position by the mass, with 
regard to sanouiuHn<^ objects, appears to us insurmountable. 
\\'t.' Iiave endeavoureil to illustrate the matter, to our own 
minds, by the action of a piece of leather brought near a red- 
liot coal. The l«>ather will be affected and motion caused, 
without the intervention of either attraction or repulsion, in 
the present sense of these terms; but this motion exhibits 
itself in an alteration qfshape^ which is not at all the case with 
the crystal. Even if the direct attraction or repulsion of the 
poles be rejected, we do not see how the exjiressed relation 
between the mairnecrystallic axis and the magnetic resultant 
is possible, without including the idea of lateral attraction 
between these lines, and consequently of the mass associated 
with the former. In the case of flat poles, the magnetic re- 
sultant is a straight line from pole to pole across the magnetic 
field. I^et us suppose, at any given moment, this line and 
the magnecrystallic axis of a properly suspended crystal to 
cross each other at an oblique angle ; let the crystal be for- 
gotten for a moment, and the attention fixed on those two 
lines. Let ns suppose the former line fixed, and the latter 
free to rotate, the point of intersection being regarded as a 
kind of pivot round which it can turn. On the evolution of 
the magnetic force, the magnecrystallic axis "will turn and set 
itself alongside the magnetic resultant. The matter may be 
rendered very clear by taking a pair of scissors, partly open, 
in the hand, holding one side fast, and then closing them. 
The two lines close in a manner exactly similar; and all that 
is required to make the illustration perfect, is to suppose this 
power of closing suddenly developed in the scissors themselves. 
How should we name a power resident in the scissors and 
capable of thus drawing the blades together? It may be 
called a 'tendency,' or an ' endeavour,' but the word a//rrtc//ow 
seems to be as suitable as either. 

The symmetry of crystalline arrangement is annihilated by 
reducing the mass to powder. "That force among the par- 
ticles which makes them cohere in regular order" is here in- 
eflfective. The magnecrystallic force, in short, is reduced to 
nothing, but we have the same results. If, then, the principle 
of elective polarity, the mere modification of magnetism or 
diamagnetism by mechanical arrangement, be sufficient to 
explain the entire series of crystalline phaenomena in the mag- 
netic field, why assume the existence of this new force, the 
very conception of which is attended with so many difficulties* ? 

* " Perhaps," says Mr. Faraday, in a short note referring to * the strange 
and striking character ' of this force, " these points may find their explica- 
tion hereafter in the action of contiguous particles." 

Magnelo-optic Properties of Crystals. 21 

Application of the principle of Elective Polarity to Crystals. 

We shall now endeavour to apply the general principle of 
elective polarity to the case of crystals. This principle may 
be briefly enunciated as follows : — 

If the arrangement of the component particles of any body be 
such as to present different degrees of proximity in different 
directions^ then the line of closest proximity, other circumstances 
beijig equal, will be that chosen by the respective forces for the 
exhibition of their greatest energy. If the mass be magnetic, 
this line ivill stand axial ; if diamagnetic, equatorial. 

From this point of view, the deportment of the two classes 
of crystals, represented by Iceland spar and carbonate of iron, 
presents no difficulty. Their crj^stalline form is the same; 
and as to the arrangement of the particles, what is true of one 
will be true of the other. Supposing, then, the line of closest 
proximity to coincide with the optic axis ; this line, according 
to the principle expressed, will stand axial or equatorial, as 
the mass is magnetic or diamagnetic, which is precisely what 
the experiments with these crystals exhibit. 

Analogy, as we have seen, justifies the assumption here 
made. It will, however, be of interest to inquire, whether 
any discoverable circumstance connectetl with crystalline for- 
mation exists, upon which the dilierence of proximity de- 
pends; and, knowing which, we can pronoiuice with tolerable 
certainty, as to the position which the crystal will take up in 
the magnetic field. 

The following experiments will perhaps suggest a reply. 

If a prism of sulphate of magnesia be suspended between 
the poles with its axis horizontal, on exciting the magnet the 
axis will take up the ecjuatorial position. This is not entirely 
due to the form of the crystal; for even when its axial dimen- 
sion is shortest, the axis will assert the equatorial position ; 
thus behaving like a magnetic body, setting its longest dimen- 
sion from pole to pole. 

Suspended from its end with its axis vertical, the prism will 
take up a determinate oblique position. When the crystal has 
come to rest, let that line through the mass which stands 
exactly equatorial be carefully marked. Lay a knife-edge 
along this line, and press it in the direction of the axis. The 
crystal will split before the pressure, disclosing a shining sur- 
face of cleavage. This is the only cleavage the crystal pos- 
sesses, and it stands equatorial. 

Sulphate of zinc is of the same form as sulphate of magnesia, 
ad its cleavage is discoverable by a process exactly similar 

22 Messrs. J. Tyndall and H. Knoblauch on the 

to that just ilescribed. Both crystals set their planes of clea- 
van;e equatorial. Both are cliama<rnetic. 

Let us now examine a magnetic crystal of similar form. 
Sulphate of nickel is, perhaps, as good an example as we can 
choose. Suspended in the magnetic fiekl with its axis hori- 
zontal, on exciting the magnet the axis will set itself from pole 
to pole; and this position will be persisted in, even when the 
axial dimension is shortest. Suspended from its end, the cry- 
stalline jirism will take up an oblique position with considerable 
energy. When the crystal thus suspended has come to rest, 
mark the line along its end which stands axial. Let a knife- 
edge be laid on this line, and pressed in a direction parallel to 
the axis of the prism. The crystal will yield before the edge, 
and discover a perfectly clean plane of cleavage. 

These facts are suggestive. The crystals here experimented 
with are of the same outward form ; each has but one cleavage ; 
and the position of this cleavage, with regard to the form of 
the crystal, is the same in all. The magnetic force, however, 
at once discovers a difference of action. The cleavages of the 
diamagnetic specimens stand equatorial ; of the magnetic^ axial. 

A cube cut from a prism of scapolite, the axis of the prism 
being perpendicular to two of the parallel faces of the cube, 
suspended in the magnetic field, sets itself with the axis of the 
prism from pole to pole. 

A cube of beryl, of the same dimensions, with the axis of 
the prism from which it was taken also perpendicular to two 
of the faces, suspended as in the former case, sets itself with 
the axis equatorial. Both these crystals are magnetic. 

The former experiments showed a dissimilarity of action 
between magnetic and diamagnetic crystals. In the present 
case both are magnetic, but still there is a difference ; the axis 
of the one prism stands axial, the axis of the other equatorial. 
With regard to the explanation of this, the following fact is 
significant. Scapolite cleaves parallel to its axis, while beryl 
cleaves perpendicular to its axis ; the cleavages in both cases, 
therefore, stand axial, thus agreeing with sulphate of nickel. 
The cleavages hence appear to take up a determinate position, 
regardless of outward form, and seem to exercise a ruling 
power over the deportment of the crystal. 

A cube of saltpetre, suspended with the crystal I ographic axis 
horizontal, sets itself between the poles with this axis equa- 

A cube o /topaz, suspended with the crystallographic axis 
horizontal, sets itself with this axis from pole to pole. 

We have here a kind of complementary case to the former. 
Both these crystals are diamagnetic. Saltpetre cleaves parallel 

Magneto-optic Properties of Crystals, 23 

to its axis ; topaz perpendicular to its axis. The planes of 
cleavage, therefore, stand in both cases e(|uatorial, thus agree- 
ing with sulpliate of zinc and sulphate of magnesia*. 

Where do these facts point? A moment's speculation will 
perhaps be allowed us here. May we not suppose these cry- 
stals to be composed of layers indefinitely thin, laid side by 
side, within the range of cohesion, which holds them together, 
but yet not in absolute contact? This seems to be no strained 
idea; for expansion and contraction by heat and cold compel 
us to assume that the particles of matter in general do not 
touch each other; that there are unfilled spaces between them. 
In such crystals as we have described, these spaces may be 
considered as alternating wiih the plates which compose the 
crystal. From this point of view it seems very natural that 
the magnetic laminae should set themselves axial, and the dia- 
magnetic equatorial ; for in crossing transverse to the cleavage, 
the respective forces would encounter the obstacle presented 
by the intervening spaces ; while in the direction parallel to 
the cleavages no such obstacle existsf. 

We have a very fine description of sand-paper here. The 
sand or emery on the surface is magnetic, while the paper 
itself is comparatively indifferent. By cutting a number of 
stripes of this paper, an inch long and a quarter of an inch 
wide, and gumming them together so as to form a parallelo- 
piped, we have a model of magnetic crystals which cleave 
parallel to their axes ; the layer of sand representing the mag- 
netic crystalline plate, and the paper the intermediate space 
between two plates. For such a model one position only is 
possible between the poles, the axial. If, however, the paral- 
lelopiped be built up of squares, equal in area to the cross 
section of the model just described, by laying square upon 
square until the pile reaches the height of an inch, we have a 
model of those magnetic crystals which cleave perpendicular 
to their axes. Such a model, although its length is four times 
its thickness, and the wholestrongly magnetic, will, on closing 
the circuit, recede from the poles as if repelled, and take up 

* Topaz possesses other cleavages, but for the sake of simplicity we have 
not introduced them ; more especially as they do not appear to vitiate the 
action of the one introduced, which is by far the most complete. 

f In these speculations we have made use of the commonly received 
notion of matter. Mr. Faraday, for reasons derived from electric conduc- 
tibility, and from certain anomalies with regard to the combinations of 
potassium and other bodies, considers this notion erroneous. Nothing, 
however, could be easier than to translate the above into a language agree- 
ing with the views of Mr. Faraday. Tiie intervals of space between the 
laminae would then become intervals of iwaAre/'/o/re, and the result of 
our reasoning would be the same as before. 

2t Messrs. J. Tyndall and H. Knoblauch on the 

the equatorial position with great energy. The deportment 
of the first model is that of scapolite; of the second, that of 
beryl. By using a thin layer of bismuth paste instead of the 
magnetic sand, the deportment of saltpetre and topaz will be 
accurately imitated. 

Our fundamental idea is, that crystals of one cleavage are 
made up of plates indefinitely thin, separated by spaces indefi- 
nitely narrow. If, however, we suppose two cleavages existing 
at right angles to each other, then we must relinquish the notion 
of plates and substitute that of little parallel bars; for the 
}ilates are divided into such by the second cleavage. If we 
further suppose these bars to be intersected by a cleavage at 
right angles to their length, then the component crystals will 
be little cubes, as in the caseof rocksaltand others. By thus 
increasing the cleavages, the original plates maybe subdivided 
indefinitely, the shape of the little component crystal bearing 
special relation to the position of the planes^'. It is an infer- 
ence which follows immediately from our way of viewing the 
subject, that if the crystal have several planes of cleavage, but 
all parallel to the same straight line, this line, in the case of 
magnetic crystals, will stand axial ; in the case of diamagnetic, 
equatorial. It also follows, that in the so-called regular cry- 
stals, in rock-salt, for instance, the cleavages annul each other, 
and consequently no directive power will be exhibited, which 
is actually the case. Everything which tends to destroy the 
cleavages tends also to destroy the directive power; and here 
the temperature experiments of Mr. Faraday receive at once 
their solution. Crystals of bismuth and antimony lose their 
directive \)o\sexjust as they melt, for at this particular instant 
the cleavages disappear. Iceland spar and tourmaline, on the 
contrary', retain their directive power, for in their case the 
cleavages are unaffected. The deportment of rock crystal, 
whose weakness of action appears to have taken both Mr. 
Faraday and M. Pliicker by surprise — as here the optic axis 
force, without assigning any reason, has thought proper to 
absent itself almost totally — follows at once from the homo- 
geneous nature of its mass; it is almost like glass, which pos- 
sesses no directive power; its cleavages are merely traces of 
cleavage. If, instead of possessing planes of cleavage, a cry- 
stal be composed of a bundle of fibres, the forces may be ex- 
pected to act with greater energy along the fibre than across 
it. Anything, in short, that afiects the mechanical arrange- 
ment of the particles will affect, in a corresponding degree, 
the line of elective polarity. There are crystals which are 
both fibrous and have planes of cleavage, the latter often per- 
* See the last note at bottom of page 23. 

Magneto-optic Properties of Crystals. 25 

pendicular to the fibre ; in this case two opposing arrange- 
ments are present, and it is difficult to pronounce beforehand 
which would predominate*. 

The same difficulty extends to crystals possessing several 
planes of cleavage, oblique to each other, and having no com- 
mon direction. In many cases, however, the principle may 
be successfully applied. We shall content ourself in making 
use of it to explain the deportment of that class of crystals, of 
which, as to form, Iceland spar is the type. 

For the sake of simplicity, we will commence our demon- 
stration with an exceedingly thin rhombus cloven from this 
crystal. Looking down upon the flat surface of such a rhom- 
bus, what have we before us? It is cleavable parallel to the 
four sides. Hence our answer must be, " an indefinite num- 
ber of smaller rhombuses held symmetrically together by the 
force of cohesion." Let us confine our attention, for a mo- 
ment, to two rows of these rhombuses; the one ranged along 
the greater diagonal, the other along the less. A moment's 
consideration will suffice to show, that whatever be the num- 
ber of small rhombuses supposed to stand upon the long 
diagonal, precisely the same number must fit along the short 
one ; but in the latter case they are closer together. The matter 
may be rendered very plain by drawing a lozenge on paper, 
with opposite acute angles of 77°, being those of Iceland spar. 
Draw two lines, a little apart, parallel to two opposite sides of 
the lozenge, and nearly through its centre; and two others, 
the same distance apart, parallel to the other two sides of the 
figure. The original rhombus is thus divided into four smaller 
ones ; two of which stand upon the long diagonal, and two 
upon the short one, each of the four being separated from 
its neighbour by an interval which may be considered to re- 
present the interval of cleavage in the crystal. The two which 
stand upon the long diagonal, L, have their acute angles op- 
posite; the two which stand upon the short diagonal, S, have 
their obtuse angles opposite. ' The distance between the two 
former, across the interval of cleavage, is to the distance be- 
tween the two latter, as L is to S, or as the cosine of 38° 30' 
to its sine, or as 4 : 3. We may conceive the size of these 
rhombuses to decrease till they become molecular ; the above 
ratio will then appear in the form of a differential quotient, 
but its value will be unaliereil. Here, then, we have along 
the greater diagonal a row of magnetic or diamagnetic mole- 
cules, or ' centres of force,' to use a term of Mr. Faraday's, 
the distance between each two being represented by the figure 

* It is probable that the primitive plates tliemselves have different ar- 
rangements of the mulecules along and across them. 

26 Messrs. J. Tyndall aud H. Knoblauch on the 

4; and along the short diagonal a row of molecules, the di- 
stnnce between each two being represented b}' the figure 3. 
In the magnetic field, theretbre, the short diagonal will be 
the line of elective polarity; and in magnetic crystals will 
stand axial, in diamagnetic equatorial, which is precisely the 
case exhibited by experiment. Thus the apparent anomaly 
ofcarbonate of lime setting its long diagonal axial, and car- 
bonate of iron its short diagonal axial, seems to be (uliy ex- 
plaineii ; the position of the former line being due, not to any 
endeavour on its part to stand parallel with the magnetic re- 
sultant, but being the simple consequence of the repulsion of 
the short diagonal. 

These conclusions are corroborated by experiment. Let a 
rhombus be cut from pasteboard, of the same shape as a 
rhombus of Iceland spar. Along the greater diagonal, fix 
six or eight small magnetic ))ellets, and along tlie short 
diagonal the same number. If this rhombus be suspended 
horizontally in the magnetic field, on closing the circuit the 
short diagonal will set itself from pole to pole. If pellets of 
bismuth be used, the same diagonal will stand equatorial. 

There is no difficulty in extending the reasoning used above 
to the case of full crystals. If this be done, it will be seen 
that the line of closest proximity coincides with the optic axis, 
which axis, in the magnetic field, will signalize itself accord- 
ingly. A remarkable coincidence exists between this view 
and that expressed by Mitscherlich in his beautiful investiga- 
tions on the expansion of crystals by heat*. "If," says this 
gifted philosopher, " we imagine the repulsive force of the 
particles increased by the accession of heat, then we must 
conclude that the line of greatest expansion will be that in 
which the atoms lie most closely together." This line of 
greatest expansion Mitscherlich found, in the case of Iceland 
spar, to coincide with the optic axis. The same conclusion 
has thus been arrived at by two modes of reasoning, as differ- 
ent as can well be conceived. 

If, then, speculation and experiment concur in pronouncing 
the line of closest proximity among the particles, to be that in 
which the magnetic and diamagnetic forces will exhibit them- 
selves with peculiar energy, thus determining the position of 
the crystalline mass between the poles, we are furnished with 
a valuable means of ascertaining the relative values of this 
proximity in different directions through the mass. An 07-der 
of contact might, perhaps, by this means be established, of 
great interest in a mineralogical point of view. In the case of a 
right rhombic prism, for example, the long diagonal oflhe base 
* PoggendorfF's Annalen, vol. x. p. 138. 

Magneto-optic Properties of Crystals. 27 

may denote a line of contact very different from that denoted 
by the short one ; and the line at right angles to the diagonals, 
that is, the axis of the prism, a contact very different from 
both. We can compare these lines two at a time. By hang- 
ing the short diagonal vertical in the magnetic field, its rota- 
tory power is annulled, and we can compare the long-diagonal 
and the axis. By hanging the long diagonal vertical, we can 
compare the short diagonal and the axis. By hanging the 
axis vertical, we can compare the two diagonals. From this 
point of view the deportment of heavy spar and coelestine, so 
utterly irreconcileable with the assumption of an optic axis 
force, presents no difficulty. It we suppose the proximity 
along the axis of the prism to be intermediate between the 
proximities along the two diagonals, tlie action of both cry- 
stals follows as a necessary consequence. Suspended from 
one angle, the axis must stand from pole to pole; from the 
other angle, it must stand equatorial. 

A ball of dough, made from bismuth powder, was placed 
between two bits of glass and pressed to the thickness of a 
quarter of an inch. It was then set edgeways between the 
plates and pressed again, but not so strongly as in the former 
case. A model of heavy spar was cut from the mass, so that 
the shorter diagonal of its rhombic base coincided with the 
line of greatest compression; the axis of the model wiih the 
direction of less compression, and the longer diagonal of the 
base with that direction in which no pressure had been ex- 
erted. When this model ivas dried and suspended in the mag- 
neticjield^ there was no recog7iizable differeiice between its de- 
portment and that of heavy spar. 

When a crystal cleaves symmetrically in several planes, all 
parallel to the same straight line, and, at the same time, in a 
direction perpendicular to this line, then the latter cleavage, 
if it be more eminent than the former, may be expected to 
predominate ; but when the cleavages are oblique to each other, 
the united action of several minor cleavages may be such as 
to overcome the principal one, or so to modify it that its action 
is not at all the same as that of a cleavage of the same value 
unintersected by others. A complex action among the par- 
ticles of the crystal itself may contribute to this result, and 
possibly in some cases modify even the influence of proximity. 
If we hang a magnetic body between the poles, it always shows 
a preference for edges and corners, and will spring to a point 
much more readily than to a surface. Diamagnetic bodies 
will recede from edges and corners. The fluid is, as it were., 
discharged with greater power from a point. A similar action 
among the crystalline particles may possibly bring about the 
modification we have hinted at. 

28 Messrs. J. Tyndall and H. Knoblauch on flic 

During this investigation a great number of crystals have 
passed through our hands, but it is useless to cumber the reader 
with a recital of them. Tiie number of natural crystals have 
amounted to nearly one hundred; while, through the accus- 
tomed kindness of Prolessor Bunsen, the entire collection of 
artificial crystals, which his laboratory contains, has been 
placed at our disposal*. 

We now pass over to a brief examination of the basis on 
which the second law of M. Pliicker rests: — the affirmation 
that the magnetic attraction decreases in a quicker ratio than 
tiie repulsion ol' the optic axes. The ingenuity of this hypo- 
thesis, and its apparent sufficiency to account for the phaeno- 
mena observed by M. Pliicker, are evident. It will be seen, 
however, that this repulsion arises from quite another cause — 
a source of error which, unfortunately, has run undetected 
through the entire series of this philosopher's inquiries. 

The following experiment is a type of those which led M. 
Pliicker to the above conclusion. A tourmaline crystal 36 
millimeters long and 4 millimeters across was brought between 
a pair of pointed moveable poles, so that it could barely swing 
between them. It set itself a^/a^. On removing the poles to 
a distance and again exciting the magnet the crystal stood 
equatorial. The same occurred, if the poles were allowed to 
remain as in the former case, when the crystal was raised 
above them or sunk beneath them. According as the crystal 
was 'withdra'-jon from the immediate neighbourhood of the j)oles, 
it turned gradually round andjinally set itself equatorial-\ . 

A similar action was observed with staurolite, beryl, ido- 
crase, smaragd, and other crystals. 

We have repeated these experiments in the manner de- 
scribed, and obtained the same results. A prism of tourma- 
line three-quarters of an inch long and a quarter of an inch 
across was hung between a pair of poles with conical points, 
placed an inch apart. On exciting the magnet the crystal 
stood axial. When the poles were withdrawn to a distance 
and the force again evolved, the same crystal stood equatorial. 
An exceedingly weak current was here used ; a single cell of 
Bunsen's construction being found more than sufficient to 
produce the result. 

According to the theory under consideration, the tourma- 
line, in the first instance, stood from pole to pole because the 
magnetism was strong enough to overcome the repulsion of 
the optic axis. This repulsion, decreasing more slowly than 

* We gladly make use of this opportunity to express our obligation to 
Dr. Debus, the able assistant in the chemical laborjitory. 
t Poggendorff's Annalcn, vol. Ixxii. p. 319. 

Magneto-optic Properties of Ciystals. 29 

the magnetic attraction, necessarily triumphed when the poles 
were removed to a sufficient distance. The same crystal, 
however, between a pair of flat poles, could }iever take up the 
axial position. On bringing the faces within half an inch of 
each other, and exciting the magnet by a battery of thirty- 
two cells, the crystal vibrated between the faces without 
touching either. The same occurred when one cell, six cells, 
twelve cells, and twenty ceils, respectively, were employed. 

If the attraction increases, as stated, more quickly than the 
hypothetic repulsion, how can the impotence of attraction in 
the case before us be accounted for? We have here a power- 
ful current, and poles only half an inch apart; power and 
proximity work together, but their united influence is insuffi- 
cient to pull the crystal into the axial line. The cause of the 
phasnomena must it seems be sought, not in optic repulsion, 
but in the manner in which the magnetic force is applied. 
The crystal is strongly magnetic, and the pointed poles exer- 
cise a concentrated local action. The ?nass of both ends of 
the crystal, when in the neighbourhood of the points, is power- 
fully attracted, while the action on the central parts, on ac- 
count of their greater distance, is comparatively weak. Be- 
tween the flat poles the crystal finds itself, as it were, totally 
immersed in the magnetic influence; its entire mass is equally 
affected, and the whole of its directive power developed. The 
similarity of action between the flat poles and the points, xvit/i- 
dra-d07i to a distance, is evident. In the latter case, the force, 
radiating from the points, has time to diffuse itself, and fastens 
almost uniformly upon the entire mass of the crystal, thus 
calling forth, as in the former case, its directive energy; and 
the equatorial position is the consequence. The disposition 
of the lines of force, in the case of points, is readily observed 
by means of iron filings strewed on paper and brought over 
the poles. When the latter are near each other, on exciting 
the magnet the filings are gathered in and stretch in a rigid 
line from point to point; according as the poles are with- 
drawn, the magnetic curves take a wider range, and at length 
attain a breadth sufficient to encompass the entire mass of the 

As the local attraction of the mass in the case of magnetic 
crystals deranges the directive power and overcomes it, so 
will the local repidsion of the mass in diamagnetic crystals. 
A prism of heavy spar, whose length was twice its breadth, 
hung from its acute angle, stood between the flat poles axial, 
between the points equatorial. On making its length and 

* Mr. Faraday has already pointed out " the great value of a magnetic 
field of uniform force."— Phil. Trans., 1841), p. 4. 

30 Messrs. J. Tyndall and H. Knoblauch on the 

breadth aUke, the axis of the prism stood from pole to pole, 
whether the conical points or Hat laces were used. Shorten- 
ing the axial direction a little more, and suspending the cry- 
stal from its obtuse angle, the axis between the Hat poles stood 
e(]uatorial, and, consecjuently, the longest dimension of the 
crystal, axial ; between the points, owing to the repulsion of 
the extreme ends, the length stood equatorial. Similar ex- 
periments were made with ccelestme and topaz; but all with 
the same general result. 

" 1 had the advantage," says Mr. Faraday, " of verifying 
Plilcker's results under his own personal tuition, in respect of 
tourmaline, staurolite, red ferrocyanide of potassium, and 
Iceland spar. Since then, and in reference to the present 
inquiry, 1 have carefully examined calcareous s])ar, as being 
that one of the bodies which was at the same time free from 
magnetic action, and so simple in its crystalline relations as 
to possess but one optic axis. 

" When a small rhomboid about 0'3 of an inch in its 
greatest dimension is suspended with its optic axis horizontal 
between the pointed poles of the electro-magnet, approximated 
as closely as they can be to allow free motion ; the rhomboid 
sets in the equatorial direction, and the ojjtic axis coincides 
with the magnetic axis ; but if the poles be separated to the 
distance of a half or three-quarters of an inch, the rhomboid 
turned through 90° and set with the optic axis in the equato- 
rial direction, and the greatest length axial. In the first in- 
stance the diamagnetic force overcame the optic axis force; 
in the second the optic axis force was the stronger of the two." 

The foregoing considerations will, we believe, render it 
very clear that the introduction of this optic axis force is al- 
together unnecessary ; the case being simply one of local re- 
pulsion. Mr. Faraday himself found that the crystal between 
the flat poles could never set its optic axis from pole to pole ; 
between the points alone was the turning round of the crystal 
possible. We have made the experiment. A fine large cry- 
stal of Iceland spar, suspended between the near points, set 
its optic axis from point to point; between the distant points 
the axis stood equatorial. The crystal was then removed 
from the magnetic field, placed in an agate mortar and 
pounded to powder. The powder was dissolved in muriatic 
acid. From the solution it was precipitated by carbonate of 
ammonia. The precipitate thus obtained, as is well known, 
is exactly of the same chemical constitution as the crystal. 
This precipitate was mixed with gum water and squeezed in 
one direction. From the mass thus squeezed a model of Ice- 
land spar was made, the line of greatest compression through 

Magneto-optic Propei'ties of Crystals. 31 

the model coinciding with that which represented the optical 
axis. This viodel imitated, in every respect, the deportment 
observed by Mr. Faraday. Between the near points the opti- 
cal axis stood from point to point, between the distant points 
equatorial. It cannot however be imagined that the optic 
axis force survived the pounding, dissolving and precipitating. 
Further, this optic axis force is a sword which cuts two ways; 
if it be assumed repulsive, then the deportment of carbonate 
of lime and iron is unexplainable: if attractive, it fails in the 
case of Iceland spar. 

It is a remarkable fact, that all those crystals which exhibit 
this phenomenon of turning round, cleave, either perpendi- 
cular to their axes, or oblique to them, furnishing a resultant 
which acts in the direction of the perpendicular. Beryl is an 
example of the former ; the crystal just examined, Iceland 
spar, is an example of the latter. This is exactly what must 
have been expected. In the case of a magnetic crystal, clea- 
vable j)arallel to its length alone, there is no reason present 
why the axial line should ever be forsaken. But if the clea- 
vages be transverse, or oblique, so as to furnish a line of elec- 
tive polarity in the transverse direction, two diverse causes 
come into operation. By virtue of its magnetism, the crystal 
seeks to set its length axial, as a bit of iron or nickel would 
do ; but in virtue of its mechanical structure, it seeks to place 
a line at right angles to its length axial. For the reasons 
before adduced, if the near points be used, the former is tri- 
umphant; if the points be distant, the latter predominates. 

We noticed in a former paper a description of gutta-percha 
of a fibrous texture, which, on being suspended between the 
poles, was found to transmit the magnetic force with peculiar 
facility along the fibre. A piece was cut from this substance, 
exactly the same size as the tourmaline crystal, described at 
the commencement of this section. The fibre was transverse 
to the length of the piece. Suspended in the magnetic field, 
the gutta-percha exhibited al! the phenomena of the crystal. 

One of the sand-paper models before described is still more 
characteristic as regards this turning round on the removal 
of the poles to a distance. We allude to that whose magnetic 
layers of emery are perpendicular to its length. The deport- 
ment of this model, if we except its greater energy, is not to 
be distinguished from that of a prism of beryl. Between the 
near points both model and crystal stand axial, between the 
distant points equatorial, and between the flat poles the de- 
portment, as before described, is exactly the same. The 
magnetic laminae of beryl occupy the same position, with re- 
gard to its axis, as the magnetic laminse oi the model, with 

82 On the Magneto-optic Properties of Crystals. 

regard to its axis. There is no difference in construction, 
save in tlie superior workmanship of nature, and there is no 
difference at all as regards deportment. Surely these consi- 
derations suggest a common origin for the phaenomena exhi- 
bited by both. 

We have the same action in the case of the compressed 
dough, fornied from the powdered carbonate of iron and bis- 
muth. A plate of the former, three-quarters of an incli 
square and one-tenth of an inch in thickness, stands between 
the conical poles, brought within an inch of each other, ex- 
actly axial ; between the same poles, two inches apart, it 
stands equatorial. A plate of compressed bismuth dough 
stands, between the near points, equatorial, between the di- 
stant points, axial. 

Any hypothesis which solves these experiments must em- 
brace crystalline action also ; for the results are not to be 
distinguished from each other. But in the above cases an 
optic action is out of the question. With the similarity of 
structure between beryl and the sand-paper model, above 
described, — with the complete identity of action which they 
exhibit, before us ; is it necessary, in explanation of that ac- 
tion, to assume the existence of a force which, in the case of 
the crystal, is all but inconceivable, and in the case of the 
model is not to be thought of? In his able strictures on the 
theory of M. Becquerel*, M. Plucker himself affirms, that 
we have no example of a force which is not associated with 
ponderable matter. If this be the case as regards the optic 
axis force, if the attraction and repulsion attributed to it be 
actually exerted on the mass of the crystal, how is it to be 
distinguished from magnetism or diamagyietism ? The as- 
sumption of Mr. Faraday appears to be the only refuge here; 
the abandonment of attraction and repulsion altogether. 

In the first section of this memoir it has been proved, by 
the production of numerous exceptions, that the law of M. 
Plucker, as newly revised, is untenable. It has also there 
been shown, that the experiments upon which Mr. Faraday 
grounds his hypothesis of a purely directive force, are refer- 
able to quite another cause. In the second section an attempt 
has been made to connect this cause with crystalline structure, 
and to prove its sufficiency to produce the particular phaeno- 
mena exhibited by crystals. In the third section we find the 
principle entering into the most complicated instances of these 
phaenomena, and reducing them to cases of extreme simpli- 
city. The choice therefore rests between the assumption of 
three nexo forces which seem but lamely to execute their mis- 
* Poggendorff's Annakn, vol. Ixxvii. p. 5/8, 

Notices of a late Visit to the Parallel Roads of Loch ah cr. 83 

sion, and that simple modification of existing forces, to which 
we have given the name elective polarityj and which seems 
sufficiently embracing to account for all. 

It appears then to be sufficiently established, that from the 
deportment of crystalline bodies in tlie magnetic field, no di- 
rect connexion between light and magnetism can l)e inferred. 
A ricli possession, as regards physical discover}', seems to be 
thus snatched away from us ; but the result will be compen- 
satory. That a certain relation exists, with respect to the 
path chosen by both forces through transparent bodies, must 
be evident to any one who carefully considers the experiments 
described in this memoir. The further examination of this 
deeply interesting subject we refer to another occasion. 

Nature acts by general laws, to which the terms great and 
small are unknown ; and it cannot be doubted that the modi- 
fications of magnetic force, exhibited by bits of copperas and 
sugar in the magnetic field, display themselves on a large 
scale in the crust of the earth itself. A lump of stratified grit 
exhibits elective polarity. It is magnetic, but will set its 
planes of stratification from pole to pole, though it should be 
twice as long in the direction at right angles to these planes. 
A new element appears thus to enter our speculations as to 
the position of the magnetic poles of our planet ; the influence 
of stratification and plutonic disturbance upon the magnetic 
and electric forces. 
Marburg, May 1850- 

II. Notices of a late Visit to the Parallel Roads of Lochaber. 
By James Bryce, Jun., M.A., F.G.S/- 

THE Lochaber glens have been subjected to so keen a 
scrutiny by the advocates for the various theories of the 
Parallel Roads, that it cannot be expected there should remain 
many facts of importance to be yet ascertained. By this cir- 
cumstance, however, the obligation upon an observer at once 
to make known such facts as may have come under his notice 
is rendered more imperative, while the value of new facts is 
enhanced. Observations, which in other circumstances would 
be scarcely deemed worthy of record, become of importance 
when viewed in connexion with an inquiry such as this, which, 
after all the discussion elicited by it, still remains the great 
unsolved problem of Scottish geology. In submitting the fol- 
lowing communication, it is not my purpose to advance a new 

* Communicated by the Author, and containing the substance of a paper 
read to the Philosophical Society of Glasgow, March 6, 1850. 

Phil, Mag, S, 3. Vol, 37. No. 24.?, My 1 850. D 

S* Mr. J. Bryce's Notices of a late Visit 

theory. I have merely in view the much more humble object 
or|)iitting on record a few facts, which seem to have escaped 
the notice of previous observers ; and of oH'ering, in connexion 
with these, some remarks on the two theories last proj)osed. 
1 refer to those of Mr. Chambers of Edinburgh, and Mr. 
James Thomson of Glasgow, both published early in 1848; 
the latter iuimediately before my visit, which took place in 
July of that year. My examination of the district had thus 
additional interest given to it, as the facts were to be viewed 
under a somewhat novel aspect, and had not yet been com- 
mented on by any geologist, with reference to their bearing 
upon the two theories in question. 

Mr. Chambers's account of the Parallel Roads, with his 
theory of their origin, forms a portion (pp. 95-130) of his 
valuable and beautifully illustrated work on Ancient Sea- 
Margins. A map of part of Lochaber, showing the shelves 
in the glens, is given at the ejul. It has been " constructed 
by iSIessrs. W. and A. K. Johnston under the direction of 
Sir George M'^Kenzie, Bart., David Milne, Esq., and Robert 
Chambers, Esq." The same map accompanies a late paper 
on the Parallel Roads, by Sir George M^-Kenzie (Ed. N. Phil. 
Journ., vol. xliv.) ; it is that to which Mr. Milne refers in his 
late important paper (Ed. N. Phil. Journ., vol. xliii. p. 339); 
and on which the reasonings of Mr. James Thonison are 
founded, an enlarged copy of it having been laid before the 
Royal Society of Edinburgh along with his paper. 

Now, this map contains an important topographical error, 
calculated to mislead those who may frame theories of the 
Roadswithouthavingmade a personal inspection of the ground. 
The error consists in this — that at its junction with Glen 
Fintec, Glen Gluoy is laid down as opening towards Loch 
Lochy ; whereas, in point of i'act, tiie high ridge descending 
from the table-land at the top of Glen Toorat, and shutting 
in Glen Gluoy on the west, continues its course southwards 
iully a mile below the point where Glen Fintec opens into 
Glen Gluoy. Glen Y'wMqcis thus completely cut off from direct 
co7inexio7i with Loch Lochy, the ridge in question being con- 
tinuous throughout, and rising to the height of from 1200 to 
1800 feet above the sea, or from 300 to 700 feet above the 
upper shelf. The rocks of which the ridge consists are chiefly 
micaceous slate and quartzite, the strata being nearly on end, 
and ransinfj in the direction of the ridge, or about S.W. 1 
could detect no traces of scratching or grooving, though the 
rocks are laid bare in many places, and strew the surface in 
huge flat masses. 

The error now pointed out involves another in the repre- 

to the Parallel Roads of Lochaher. ^5 

sentation of a portion of the upper shelf. The eastern portion 
is correctly represented as terminating at the south-west corner 
of Glen Fintec ; but on the west side, the shelf, instead of ter- 
minating as expressed on the map, is continued a considerable 
distance southwards of the opening of Glen Fintec, from lialf 
a mile to a mile, or perhaps more; at first less distinct than 
usual, then more plainly marked, till coming against a rocky 
projecting ledge on the hill side, it fails as usual to impress it, 
and is seen no more. 

On referring lately to Sir T. D. Lauder's map accom- 
panying his paper (Trans. Roy. Soc. Edinb. for 1817), which 
I had not looked into before visiting the Parallel Roads, I 
found that his representation of this portion of the district is 
much more correct. Glen Gluoy is given in its true dimen- 
sions; and the stream formed by the union of the Gluoy 
and Fintec waters is laid down as turning, at a place called 
Lowbridge, round the southern termination of the moun- 
tainous ridge just described, and discharging into Loch Lochy, 
nearly opposite to a village named Kyle-Rose in Mr. Cham- 
bers's map. This representation is very near the truth ; but 
perhaps too great extension is given to the southern part of 
Loch Lochy. 

One of the principal objections which has been urged against 
Mr. Milne's theory, is the absence from the district of a suffi- 
cient quantity of detrital matter to account for the barriers at 
the mouths of the glens, required by the theory. The force 
of this objection would be very much diminished, if we could 
receive Mr. Chambers's account of the hill of Oonchan as cor- 
rect. It appears to me, however, that he quite over-estimates 
the amount of detritus in this hill. 

After giving a full and accurate description of the other 
principal detrital accumulations of the district, Mr. Chambers 
thus notices the hill of Oonchan : — " By far the grandest delta 
of the district is that hill which has been referred to under 
the name of Unichan as occnpying so much of the lower part 
of Glen Spean. This is a mass of gravel 11 miles long by 
perhaps 2 broad, and reaching an elevation of 612 feet. I 
observed rock rising through it at one place; but it is mainly, 
as has been said, a hill of gravel." He considers that " when 
the sea stood somewhat above 622 feet (and there is evidence 
of its having paused long at 628 or 630), the rivers descending 
from the Ben Nevis group of mountains delivered their spoils 
into the estuary filling Glen Spean : on the withdrawal of the 
sea this mass was left." 

The high ground in question, part only of which is called 
Oonchan, is an undulating ridge parallel to the main chain, 


36 Mr. J. Bryce's Notices of o late Visit 

and siietcliing from near Fort William to within 1,} mile of 
the bridive of Hoy, a distance of about 12 miles. Such sub- 
oriiinate elevations are seen at the base of almost every high 
chain, and mark the axes along which the upheaving forces 
acted with decreasing intensity. This ridge is separated from 
the main chain by a slightly depressed tract, having a very 
smooth outline, into which five glens descending from the Ben 
Nevis group open at right angles, the surface presenting no 
marked change of character at the junction. The streams 
from these glens, as well as those which drain the tract itself, 
being prevented by the high ground in front from following 
direct courses to the valley of the Spean, are deflected to the 
east and west, ])arallel to the high ground on eidier side. The 
watershed of the tract being nearer the western than the east- 
ern end, and the inclination eastwards slight, there is an im- 
perfect discharge of the waters, and consequently extensive 
swam})s have been formed, which sometimes become lakes. 
The annexed sketch will give an idea of the outline of the 

a. Steep slope of the Ben ^\ H 

Ne\is group. '^ 

4. The hollow, or swampy 

r. Swelling top of the ridge. 

d. Sides of Ooiichan. 

e. River Spean. 
/. Slopes ascending towards 


On the western part of the ridge the rock is seen in many 
places; and about the middle I found it a little lower than 
the highest point, c, of the ridge at that part; and I think 
there can be little doubt that the thickness of the detrital 
covering is in most places inconsiderable. At its eastern ter- 
mination detritus appears in more imposing quantity. Near 
the bridge of Roy the end of the ridge is cut through by 
numerous streams, or rather the channels of streams; for 
there is often no water, and the detritus stands out in nume- 
rous round or elliptic flat-topped mounds with steep sides. 
Towards the base of Cruachaninish and Benchilinaig these 
are smaller, and of rounder forms, resembling Danish raths j 

to the Parallel Roads of Lochaher. 37 

while further back the detritus only shows itself in terraces, 
formed by the streams ciittinij into the tahis at the base of the 
high mountains. 

Mr. Chambers regards the question of the oiigin of liie 
Parallel Roads as " involved in that of the superficial forma- 
tions generally, which bear the marks of former levels of the 
sea at various intervals up to 1200 feet;" the various mark- 
ings in the three kingdoms, in France, &c., " all falling into 
such conformity as to prove that the shift of level has been 
efiected from at least that height with perfect equability 
throughout." He considers this widely extended and strongly 
marked conformity " as more favourable to the idea of a re- 
cession of the sea as opposed to that of an elevation of the 
land, since it is precisely what would result from the former 
operation, while there is an obvious difficulty in supposing" 
that so large a portion of the earth's crust could be repeatedly 
upheaved, and yet the relative levels so preserved " that be- 
tween Paris and Inverness not a vertical loot of derangement 
could be detected." 

The explanation of the origin of the Parallel Roads is thus 
mixed up with, indeed forms an essential part of, his general 
theory. And whatever difficulty geologists may feel in giving 
their assent to such generalizations as those just quoted, or how- 
ever unwilling they may be, in the present state of inquiry, to 
admit many successive equable sinkings of the waters of the 
ocean all over the globe, the same difficulties and hesitation must 
be experienced in receiving Mr. Chambers's explanation as the 
true theory of the Parallel Roads. Besides, the speciality of 
the phaenomena is by no means accounted lor on this hypo- 
thesis. It appears to me to require a special local cause. 
On the hypothesis of the shelves being formed by the sea, it 
cannot, 1 think, be shown why other Highland glens were not 
equally impressed ; or that any conservative influences have 
operated in Lochaber, which were not just as likely to prevail 
in other places. This argument cannot be properly estimated 
by one who has not seen the shelves in Glen Roy and Glen 
Gluoy ; from examining sea and lake-terraces, from descrip- 
tions and drawings, the faintest conce})tions only can be formed 
of the wonderful reality. Any one on whose view the scene 
which is presented on turning the flank of Bohuntine hill, 
bursts for the first time, must look with the deepest astonish- 
ment at the distinctness, continuity, and extent of the shelves ; 
he will feel how inadequate were all his conceptions, and 
how little the Parallel Roads have in common with any appear- 
ances which have come under his notice before. Mr. Cham- 
bers eloquently describes the first impressions, and acknow- 

38 Mr. J. Bryce's Notices of a late Visit 

ledges the " singular distinctness " of the shelves in this loca- 
lity; yet his theory affords no explanation of a phenomenon 
so remarkable. But this argument has been so ably handled 
by Mr. Milne in his reply to Mr. Darwin (Ed. N. Phil. Journ., 
vol. xliii. p. 4^7), that it is unnecessary to insist further 
upon it. 

The faint and higher markings on the south side of Glen 
Spean, which Mr. Chambers lays so much stress upon as sup- 
porting his view, I did not notice. "The whole," he says, 
" might appear doubtful to many persons ; in an unfavourable 
light, a hasty observer might pass them by altogether unno- 
ticed." These may have been my circumstances, and 1 do 
not therefore question the existence of such markings; but I 
cannot regard the conclusion as warranted by the tacts — the 
existence, namely, " in Glen Spean of a body of water at 
levels above the barriers assigned to it by M'^Culloch, Lauder 
and jNIilne." Are not these and similar slight and local mark- 
ings best explained on the received theory, — the action of cur- 
rents upon the submerged land, or the occasional pauses in 
the process of elevation? 

While thus dissenting from the theoretical conclusions at 
which Mr. Chambers has arrived, I cannot forbear to express 
my high admiration of his patient and active research, — his 
clear, truthful, and eloquent descriptions, — and of the service 
he has rendered to geology by his many exact measurements, 
and by proposing a theory which will lead to a more careful 
study of phaenomena of this class. 

The lake theory has gained immensely of late by the ad- 
vocacy of Mr. David Milne. His paper, already reli?rred to, 
is perhaps the most able which has been written upon the 
Parallel Roads. The evidence in support of his Own views has 
been collected with the greatest sagacity, and the arguments 
founded upon it conducted with consummate skill ; while he 
appears to me. to have completely demolished both the theory 
of iSIr. Darwin, and the glacial theory, in the form proposed 
bij M. Agassiz. The agency assigned by Agassiz will not 
explain all the phsenomena, and is positively inconsistent with 
many facts. But it does not hence follow that glacial action 
is to be rejected, as explaining the blocking up of the mouths 
of the glens, — for it is required for this purpose alone. May 
not a form be given to the theory vvhicli will adapt it to all 
the exigencies of the case, and thus remove from the lake 
theory the one great remaining objection — the origin and the 
disappearance of the enormous earthy barriers at the mouths 
of the glens? Since Agassiz wrote, the question has been 
placed on a very different footing. The first glacialist in 

to the Parallel Roads of Lochaber. 39 

Europe, Prof. J. D. Forbes, has given it as his decided opinion 
that glaciers formerly existed on the Cuchnllin hills in iSkye 
(Ed. N. Phil. Journ., vol. xl. p. 79). Wiiy, then, may not 
masses of ice have filled the still higher valleys of the Ben 
Nevis group of mountains? Professor Forbes'? late discoveiies 
in Switzerland respecting the viscidity of glacier ice, and the 
nature of glacier motion, appear to have suggested to Mr. 
James Thomson the highly ingenious modification of the 
glacial theory lately proposed by him (Ed. N. Phil. Journ., 
vol. xlv. p, 49). The gist of this theory is contained in the 
following passage: — 

" In Switzerland the mean temperature of the compara- 
tively low and flat land is so much above the freezing-point, 
that the ice no sooner descends from the mountains than it 
melts away; and it is thus usually prevented from spreading 
to any considerable extent over the plains. In the Antarctic 
continent, on the contrary, the mean temperature is nowhere 
so in'gh as the freezing-point. The ice, therefore, which de- 
scends from the hills unites itself with that which is deposited 
from the atmosphere on the plains; and the whole becomes 
consolidated into one continuous mass, of immense depth, 
which glides gradually onwards towards the ocean .... Now 
a climate somewhere intermediate between these extremes 
appears to be that which would be requisite to form the shelves 
in the glens of Lochaber. The climate of Switzerland would 
be too warm to admit of a sufficient horizontal extension of 
the glaciers ; that of the Antarctic continent too cold to allow 
the lakes to remain unfrozen. If the climate of Scotland were 
again to become such that the mean temperature of Glen 
Spean would be not much above the freezing-point, there 
seems to be every reason to believe that that glen would again 
be nearly filled with an enormous mass of ice; while its upper 
parts, and also Glen Roy, would be occupied by lakes . . . ." 

The state of things here supposed is extremely critical ; not 
likely long to maintain itself'under the same geographical dis- 
tribution of the surface as now prevails, and liable to be 
changed by many slight causes. If the mean temperature of 
Glen Spean was little above freezing, and wide fields of ice 
covered its surface, it is not probable that the lakes in the 
glens, at considerably higher levels, would long remain unfrozen; 
and if the Ben Nevis group of mountains, whose mean height 
we may take at somewhat less than 4000 feet, not oidy nou- 
rished glaciers in their higher recesses, but were wholly enve- 
loped in sheets of ice, can we suppose that the mountains sur- 
rounding Glen Roy and Glen Gluoy, many of which attain 
the altitude of from' 2000 to 2500 feet, would not likewise give 

40 Mr. J. Bryce's Notitrs of a late J'isif 

oriirin lo masses of ice, descending; into the tjlens, and occu- 
pyinij^ the very sites of our supposed lakes? On the other 
hand, it may be stated in lavourof Mr. Tl)omson's views, that 
tiie hypothesis of Glen iSpean hein<^ " fd led with an enormous 
mass of ice" uhich would block up Glen Hoy, is more con- 
sistent with the geography of the district, than the supposition 
that a glacier descended Irom one of the liigh valleys of the 
Ben Nevis group, and forced its way into the opening of Glen 
Koy. There is nothing in the nature of the country to deter- 
mine a glacier to follow such a course. Tiie form of the sur- 
face bctw een the Lochaber glens and the Ben Nevis group is 
such, that if a glacier descendcel from any one of the five 
great glens, whose directions are inclined to that of Glen Hoy 
at an angle of 60 or 70 degrees, and readied the open country 
at the base of the mountains, there would be nothing to deter- 
mine its course np Glen Roy, or indeed in any one direction 
more than another, except the slight eastward and northward 
slope already described. Glaciers descending from these 
glens would thus coalesce into one huge sheet, coextensive 
with the valley of the Spean. The hypothesis of sheets of ice 
covering the whole surface — " des grandes nappes de glace " — 
seems also more consistent with the absence of "perched 
blocks " and moraines, than the idea of separate glaciers. 
These are not seen anywhere over the surface of the open 
tract between the mountains and the river; and the peculiar 
detrital covering is very like that which would be formed under 
such advancing sheets, most of it being stratified sand and 
small gravel, the result of wearing, or decomposition i7i situ. 
Mr. Thomson's explanation of the phaenomena of Glen 
Gluoy is very ingenious. It will be remembered that these 
are peculiar. The shelves do not correspond with those in 
the other glens; and while in the latter each successive shelf, 
as we descend, extemls further down the glens than those that 
are higher, in Glen Gluoy the upper shelf extends further 
towards the mouth of the glen than the lower; and this lower 
shelf, unlike all the others, is not in connexion with any sum- 
mit level. If the lake theory be true, it will follow from these 
facts that the barrier which retained the water at the lower 
level was further up the glen than that which retained it at 
the higher; and that when the lower shelf was forming, the 
overflow must have taken place at the mouth of the glen. 
Mr. Thomson supposes " that the glacier which occasioned 
the formation of the higher of the Glen Gluoy shelves had at 
some former period protruded a terminal moraine as far up 
the glen as the termination of the lower shelf; that, on the 
final retiring of the glacier, this old moraine served as a bar- 

to the Parallel Roads oj Lochaher. ^l 

rier to dam up the water to the level of the lower shelf, and 
that it has been subse(|uently washed away by the river flowing 
over it." He then suggests that the space between the termi- 
nations of the upper and lower shelves sliould be examined, 
to ascertain if the remains of such a moraine exist. I made 
this examination with considerable care, but could find no 
such remnants. There is some detritus in the main glen op- 
posite the mouth of Glen Fintec; but it has obvious reference 
to the present drainage, and is in no way remarkable. The 
whole of Glen Gluoy is indeed singularly free from detritus; — 
a peculiarity which I consider due to its form. It is narrow, 
and the liills rise steep and high from the very margin of 
the river, so that there is no space wliere detritus could rest ; 
and it is thus swept away as soon as it is brought down. This 
circumstance is also favourable to the rapid and complete 
removal of such a moraine, or barrier, as Mr. Thomson sup- 
poses may have once existed. The mouth of the glen is 
equally free from detritus, or other indications of the existence 
of earthy barriers in a former condition of things. 

" A glacier occupying the present site of Loch Lochy, and 
receiving supplies from the neighbouring mountains, would 
appear," Mr. Thomson says, "to afford a sufficient explana- 
tion of the phaenomena observed in this glen." This was 
probably written under the impression that Glen Fintec com- 
municated with Loch Lochy, and that the mouth of Glen 
Gluoy was in the way of a glacier advancing from that lake. 
But this is not the case. A glacier having its origin among 
the high mountains to the N.W. of Loch Lochy — the only 
hills high enough to produce one — and advancing from Loch 
Lochy, must make its way past Maucomer and Brecklech up 
the valley of the Spean, for so only will the levels permit. 
This direction is about perpendicular to that of Glen Gluoy ; 
and it would be only a lateral branch or arm, parting from 
the main body, that could penetrate that glen. The mouth 
of the glen is narrow, and the hill sides rise steep and high; 
a little way up there is a considerable bend before we reach, 
at a mile's distance, the bosom or sinus in the hill side, where 
the moraine is conceived to have existed in connexion with 
the lower shelf. All this shows the improbability of a moraine 
being deposited at this place; and that recourse may as well 
be had to the masses of ice with which Glen Spean has been 
supposed to be filled, from its chief source in the Ben Nevis 
group. But it seems impossible that such masses of ice could 
deposit a moraine in the situation required ; and it even ap- 
pears doubtful whether sheets of ice would deposit moraines 
at all. 

d-2 Dr. Ballot on the iniporf ance q/'Dev'n\iious Jrom the mean 

I do not ("eel myself competent to express a decided opinion 
upon this "vexed (piestion;" but rejfardin^ the lake theory 
as (he true one, I think it now only renuiins to be determined 
whether the barriers at the niouths ot" the glens consisted of 
ice or of earthy materials. Perhaps we know nearly as much 
iegardin<^ the latter as we ever can know; but the valley of 
the Spean has never been carefully examined, with reference 
to the former passage of glaciers through it, by one fully com- 
petent to the task. Till this has been done, geologists are 
not in a position to decide between the rival theories. 

III. On the great importance o/' Deviations y/owi the mean 
state of the Atmosphere for the Scioice of Meteorology. By 
Dr. Buys Ballot*. 

THERE are some points in meteorology which certainly 
are no longer disputed, but which nevertheless are not 
always sufficiently present to the minds of meteorologists, nor 
so })ublicly pronounced and admitted as to compel them to 
action, and serve as a torch to illumine the path leading to 
the penetralia of science. Though these facts may appear 
simple, {particularly in England, where they have been treated 
upon, still even there it cannot be considered superfluous to 
view them in another light, and to introduce them in connexion 
with a Dutch prize question, which, in my opniion, is the 
most important meteorological question that can be brought 
forward, and which fully characterizes the new meteorological 
period developed by Dove. 

On the other hand, England has such boundless merits as 
to meteorological observations, and has such great facilities, 
in consequence of her extensive influence and wide-spread 
observatories, for the application of those facts in all parts 
of the earth, that she has a right to receive information, 
through her own periodicals, of what is taking place on the 
continent. I therefore decided (on being solicited by the 
Society of Physics of Berlin to send in annually a report of, 
and opinions on, what might occur in meteorology) to adopt 
also for insertion in an English periodical, by moditying some 
points of less interest, a paper drawn up for the Journal of 
the Society, Die Fortschritte der Physik. The truths to which 
1 allude were particularly remarked by me in 184-6, when I 
wrote my work hes Changements Periodiques de Temperature 
dependants de la nature du Soleil et de la Lune deduits d^ob- 
servations Neeiiandaiscs de 1729-1846, in which those parti- 

* Coraiiuinicated by the Astronomer Royal. 

slate of the Atmosphere for the Science of Meteorology. 43 

ciilars are to be found, chapter vii. p. 104< et seq. But let us 
proceed to those propositions. 

I. The average temperature whicii prevails at any certain 
place is not that which is generated there by the action of the 
sun, &c., and which woultl depend simply on the latitude and 
the elevation of the ground, but is remarkably changed by the 
influences of other regions, particularly by the action of the 

II. That average temperature, such as it is obtained any- 
wliere from observations during a series of years, for the dif- 
ferent months or days of the year, will by no means always 
prevail at those places for the determined month or day of 
each single year. On the contrary, observations give gene- 
rally great variations; and it is precisely the magnitude of 
these variations which it is of the utmost importance to learn. 

III. ^^^hat we asserted regarding the temperature in pro- 
position II. applies equally to all meteorological indications; 
it is of great importance to become acquainted with those va- 
riations of the barometer, and of the force and direction of 
the wind. 

IV. The most efficient means for prognosticating the 
weather are, the employment of the electric telegraphs and of 
self-registering instruments, because they facilitate and make 
possible a tabular union of the variations mentioned ni II. 
and III. 

In the following remarks these propositions are more fully 

Art. 1. No one can call in question our first proposition, 
we shall not therefore demonstrate it; we will only observe, 
that it is the winds that modify this temperature; we will en- 
deavour to ascertain how much is to be ascribed to each wind. 

Let represent for longer, 9 for shorter spaces of time, the 
mean theoretical temperature of a place, and let MT and mt 
represent the mean temperature deduced from long series of ob- 
servations^ OT and ot the observed mean temperature for that 
longer or shorter space of time at the same place in a given 
year ; then we need only annex some distinctive symbols to 
these three signs in order to show of which space of time we 
are speaking. Therefore, when we speak of years or seasons, 
we shall annex the first letters of the wordsyear, y\ 'winter^ xv\ 
spring, sp. ; summer, su, ; autu?n?i, a, at the foot of the great 
letters; and when we speak of months, we shall annex the 
first letter of the name of the month after the small letters. 
Thus Qy will signify the mean temperature of the year, fi/'the 
mean temperature of February, which ought to prevail at a 
certain place, if that place did not receive vvarmlh from and 

4-1 Dr, BuUot o;/ the importance of Dev'iaUons Jioin the mean 

ini|xirt warmlli lo the sui roiiiulinjr parts : it will readily be per- 
ceived that these values must ever be the same lor each place 
situated in the same latitude and elevation above the sea. On 
what docs it depend that MT// and »it/'i\re not found alike in 
all the places in the same parallel, but always dillerent in every 
diderent place; lower in this, higher in that, than W/y and 
6/? If there was a parallel circle which extended wholly over 
a continent, or if we passed regularly over a }oarallel circle in 
a ship, and if we. determined the M'ii/ in n different selected 

places, then would — be nearly expressed by ©y ; the 

value so obtained would, however, be somewhat greater than 
Si/, because there is more air drawing towards the north than 
towards the south over a whole parallel circle, that southern 
air at tiie same time being warmer ; and also because, near 
the equator, the latent heat which is employed in the vapori- 
zing of water is greater than tiiat which is freed by rain ; and, 
on the contrary, in higher latitudes there is more freed than 
expended on the formation of vaj)Our. This is also a cause 
why on the land 0j/ must be something less than at sea. If 
we would nicely calculate this influence, we ought equally to 
distinguish between rain that is formed in different altitudes. 
Properly we ought to infer theoretically Sy, and equally so 
S/', from the warmth which emanates from the sun to us every 
day; from the warmth which every day and night issues from 
beneath the surface of earth ; and from the warmth that is 
produced by animals, consumed by plants, lost by radiation, 
given by condensation of vapour. The difference between @j/ 
so obtained, and MTj/, (MT?/— ©j/), at a certain place, is to be 
ascribed to the influence of the wind during the year; simi- 
larly, 7ntf—S/ is the influence of the wind which prevails in 
February at that place. How far we are as yet from such a 
determination may be seen, ibr example, from the meteorology 
of the late illustrious Daniell. But even if it could be ob- 
tained, it would, however, not be fit for a great space of time; 
for certain it is, that the resultant of the winds ot a whole year 
would not have the same influence on the temperature as the 
different components. This will appear niore evident to any 
one who directs his attention to the differences 7«/j/— 6j/, 
mtf—^f\ mtjL — ^jl^ &c. He would find, not only for every 
place, but also for every month of the year, different influences 
for the same wind ; the same wind producing a different cool- 
ing or heating power in different seasons, a circumstance of 
which account is not taken in computing the resultant. 

Art. II. We will suppose that not only and 5, but also MT 
and mt were obtained at a certain place from a long series of 

state of the Atmosphere for the Science of MeteorologTj. 45 

observations, that MT therefore could be considered as the 
equilibrial state of temperature at a determined season of the 
year at that place; then we should find that the differences 
OT — MT, 0/— w//are to be ascribed to these circumstances : — 
Ist, that tlie winds had not in that space of time the same 
direction as usual; and 2nd, that the distribution of tempe- 
rature at the surrounding places was quite different from the 
usual distribution during that space of time, or shortly before. 
Thus it is necessary that we know the variations, not only lor 
the place itself for which we desire to explain the temperature, 
but also for tiie surrounding places, since the variations at the 
first place must be explained partly from the variations at the 
latter. The most important causes are always to be sought 
in the variations (deviations); it is from those that we must 
derive the exhibition of the state of temperature, not from the 
absolute observed temperature. Even now, when we give 
absolute temperatures, we do in fact give deviations ; namely, 
deviations from the arbitrary zero of temperature. Positive 
prognostications will always be given under the Ibrm of de- 
viations, and best by deviations from the mean state of the 
atmosphere. Certainly it were to be wished that we better 
understood the theoretical temperature (©), which must take 
place for certain soils and elevations above the sea, and for 
every latitude, in order also to be able to give the deviations 
from those theoretical values; but for want of that knowledge 
the deviations from the mean value are the main points for con- 

Art. III. Temperature is that state which most attracts 
the attention of the public, in consequence of the immediate 
influence it has on the relations of human life; but scientifi- 
cally, all states are equally important. The pressure of vapour 
is perhaps the most uncertain element, and of which we can 
give little ex})lanation, from the manner in which it is mea- 
sured ; electricity is not anywhere (with exception of Brussels 
and Kew) sufficiently knovvn either as to its origin or as to its 
quantity ; it is not therefore expected that the deviations of 
these elements can be given. It is the winds that bring us the 
warm air and cold waves ; they must be accurately noted as to 
direction and.strength, but it will avail little to give their devia- 
tions from the mean direction; the winds must therefore be 
noted with their real directions. On the contrary, as to the 
barometer, the deviations again are of the greatest importance," 
especially as here the theoretical state is known for every lati- 
tude. Everywhere, where attention has been paid to the de- 
viations of the barometer, which at the same time have been 
observed at different places or successively at the same place, 

+(i Dr. Ballot on the iiupoytance of Y)Q\\Q.i\ons from the mean 

it lias led, in connexion with llie observation of the wind, to 
practical tliscoveries. Who knows not the Iruits of the labours 
of UccHielcl, Kcitl, Piddin<j;ton, Thoni ? In later times also, 
the investigations of Mr. Birt on the atinos})heric waves, which 
in November pass over Eni^land and Europe, are only de- 
duced from the knowledge of the deviations. 

As we must give so much importance to the deviations of 
the baiometer and thermometer as to assert that they are ap- 
})licable in most meteorological investigations; as we further 
consider how much trouble it causes for a calculator to sub- 
tract the value obtained from every observation which he uses 
from the mean value at that place for that day, whilst the 
observer can so very easily, whilst he is noting his observa- 
tions, note in a column next to it the difference from the mean, 
we dare propose and urgently invite the observer everywhere, 
where the mean of each day is sufficiently known, or even 
where this is known with some approximation, to take this 
little trouble. We should then, alter a lapse of five or ten 
years, be able to modify the mean of the temperature, and 
then to determine it with greater certainty. A book that con- 
tains such means for every day of the year for many places 
would certainly be a most useful book; and if one once pos- 
sessed that, then it would be sufficient for the observers to 
communicate the deviations ; from time to time the correc- 
tions could be published in the form of supplements. 

Art. IV. England has given the example of communicating 
the state of the weather* at a certain instant in all parts of the 
country, at least to Glasgow, by means of telegraph, as I saw 
to my surprise in the Greenock Dailij Nexvs. My propo- 
sition made in the Changcments de Temperature was actually 
in operation. Later I have also learned that that plan is like- 
wise proposed to the British Association : thus the communi- 
cation of the weather becomes more scientific than it hitherto 
had been. Telegraphs can, better than self-registering instru- 
ments, answer the purpose of approaching to a foretelling of 
the weather at all places before it exists there ; they give us 
the opportunity of being informed of the weather before it has 
passed from one place to another. We can be on our guard 
and arrange our occupations (our observations in the first place) 
accordingly; remarkable jihaenomena will be noticed by dif- 
ferent observers in corresponding manners at different places, 
and many other advantages will result. It is true, we shall 

* This publication was principally planned and is carried into execution 
b}' the proprietors of the London Daily News. The report of the state of 
the weather at 9'' in the morning at numerous places is published every 
day in that journal. — G. B, Airy. 

state of the Atmosphere for the Science of Meteorology. 47 

be able likewise to see from the graphic self-registering instru- 
ments the state of the weather at every instant at all places 
where they exist (and this is the main point of agreement of 
both), bnt only long after those circun^slances are past; from 
the telegra[)hs we are accjuainted with it iustantaneouslij. It 
will yet be sometime^ we avow it, before we become sufficiently 
acquainted with the laws of the transit of the states of the 
weather, to be able to foretell with any certainty even from the 
known state of the weather at the neighbouring places (particu- 
larly, also, because to the class of "surrounding places" belong 
the places above us, and the winds and temperature reigning 
there) ; but we shall never arrive at this point except by means 
of exhibition of simultaneous observation. When we draw a 
series of theoretical deductions from a given distribution of 
meteorological indications (wind, heat, pressure, &c.), and 
compare them with the subsequent distribution which is really 
found to follow as an effect of the first, we cannot fail to pe- 
netrate better the origin and influence of the winds, and more- 
over the variations of temperature produced by them. 

Therefore it will be of importance to improve our graphic 
methods of representing simuhaneous observations, and either 
by that means or by numbers to exhibit those states in a 
tabular form. As to the graphic method, it is to be seen in 
the articles of Mr. Birt, Report of the Meeting of the British 
Association, 1844-, 184-5, &c., that there is a want of a uniform 
method for noting three or more variations at the same time. 
A good graphic method would have enabled Mr. Birt to com- 
municate more in fewer pages, and to put every reader in a 
state to try his conclusions and to extend them. 

Martins, in his annotations to the translation of Kamtz, has 
endeavoured to exhibit more than three variations at the same 
time; but that method, in our opinion, is not very clear. 

Since the investigation of the great November atmospheric 
wave is probably to be continued, it is perhaps not inconsistent 
to propose another manner of exhibiting it. We can form a 
map of all the places where observations are made, and give 
to each place a sign, for example («), {b\ &c. ; then the posi- 
tion of those signs in the other part of the drawing must ex- 
press the height of the barometer at those so indicated places 
in the following manner. Let us draw round that map a circle, 
which we consider as the section of a vertical cylinder, in the 
plane of which those places are situated; let us further sup- 
pose that at the places {a) {b) the barometers are placed with 
the lower surface of the mercury in the same plane of that 
circular section; so will the top of the highest standing baro- 
meter lie in a plane parallel to the first, and give a circular 

4-8 Dr. Ballot on the ituporlance of V)c\\i\\.\ow% from the mean 

section of the cylinder; the distance between the two circles 
will be proportional to the height of the barometer at that 
place. This will be true for all places; and the height of the 
letters or signs [a) (A) noted at the respective sections in the 
surface of the cylinder would inilicate the height of the baro- 
meter at those places, II we imagine our eye in the axis of 
the cylinder, anil we project those siijiposed points [a) [b) 
on the horizontal plane, or what is the same thing, if we apply 
the method of descriptive geometry to this, the greater or 
lower height of the barometers at {a) {b) will be represented by 
points, a, 3, in circles concentric with the first, but more or 
less removed, whose distance from the first [X.\\q difference of 
the radius* will be proportional to that height. So the first 
circle may represent a very low barometrical height, as 730 mil- 
limetres, and each millimetre that the barometer in {a) or [b) 
is higher may be represented by one or two millimetres' di- 
stance of the circle (a) or (3^ from the first. But we can go a 
step further; we can divide those circles from the common 
centre point into a number of sectors, thirty sectors 1 suppose: 
in one sector the letters may signify the height of the baro- 
meter at the 20th of October, in another at the 21st, and so 
on ; every sector may be applied to one day. So we shall 
have the barometrical range at every one place, and the differ- 
ent states at the different places simultaneously, equally well 
and clearly represented, while the map within the circle indi- 
cates the distribution with respect to the surface of the earth. 
If, bv chance, the points {a^ in the diilerent sectors lie in a 
circle, it indicates that the barometer at a has not varied du- 
ring the month, if they lie in an ellipse, then there have been 
two highest and two lowest states ; we see immediately those 
height's and the dates. So, as to the simultaneous comparison 
of the barometer heights, the eye catches immediately the let- 
ters that are higher or lower, and we see on the map in the 
middle the line of places where the barometer was at the high- 
est or the lowest. If there actually is a wave, then it is clearly 
exhibited thus to the eye; if the eye has difficulty in discern- 
ing the wave, then probably there is no wave, or perhaps that 
wave must have been marked out by the foregoing or following- 

It is even possible to go a step further, and, for example, 
to represent at the same time the thermometer state by the 
distances at which we set the letters (r/), [b) (the signs of 
the places) from the radii which divide the circle; the more 
on the right, for example, the higher the state of the ther- 
mometer.' It is evident, liowever, that the more variations 
we exhibit, the more is lost in simplicity. We could have 

state of the Atmosphere for the Science of Meteorology. 49 

represented also latitude, longitude, time, barometer, ther- 
mometer. How much soever we improve the graphic repre- 
sentation, we must however always, where there is not merely 
a view required but an accurate calculation, have recourse to 
a tabular exhibition. To promote this, the Utrecht Provin- 
cial Society for Arts and Sciences has issued the following 
prize question: — 

Since the usual indications of ihermometer, barometer, and 
anemometer throughout the year, that is, the periodical func- 
tions by which those indications are expressed, are now known 
for a great number of places, at least with approximatioji, and 
thus a sufficient basis is laid for the investigation of non- 
periodical changes; the Society wishes — 

After having calculated the mean indications of thermo- 
meter, barometer and anemometer, over as great a number of 
places as possible in Europe and Asiatic Russia for periods of 
five days for two successive years, — 

1. The deviations of thermometer and barometer from their 
above-described usual state in each of those periods, should 
be united in tables; 

2. The manner of transit of those deviations in time and 
space should be investigated ; and 

3. Those deviations should be compared and brought in 
connexion with the winds that prevailed during each of the 
said periods, and with the deviation from their usual direction 
which they exhibited. 

The importance of this prize proposition in connexion with 
the various researches which are required for its investigation, 
has induced the author of this question to augment the offered 
prize with one hundred and fifty guilders. It is wished that 
the answer be received before October 1, 1851, by M. C. von 
Marie, Secretary of the Utrecht Provincial Society for Arts 
and Sciences. The name of the author, as usual, in a sepa- 
rate letter. 


Postscript. — I have not mentioned in my memoir that the 
observations instituted by the Royal Society have lately been 
computed, and that the means of each month are in fact sub- 
tracted from the mean of the months of the same name. I 
had not seen the last part of the Philosophical Transactions 
in which these computations are placed. 

Phil, Mag, S. 3. Vol. 37. No. 247. July 1850. E 

C 50 ] 

IV. On the Triad ic Arrangements of Seven and Fifteen 
Things. By A. Cayley, Esq.* 

r'l^HERE is no difficulty in forming with seven letters, 
J- a, b, c, d, e, f, g, a system of seven triads containing 
every possible duad ; or, in other words, such that no two 
triads of the system contains the same duad. One such system, 
for instance, is 

abc, ade, afg, hdf, beg, cdg, cef\ 

and this is obviously one of six different systems obtained by 
permuting the letters «, b^ c. We have therefore six different 
systems containing the triad abc ; and there being the same 
number of systems containing the triads abd^ abe^ abf^wiXabg 
respectively, there are in all thirty-five different systems, each 
of them containing every possible duad. It is deserving of 
notice, that it is impossible to arrange the thirty-five triads 
formed with the seven letters into five systems, each of them 
possessing the property in question. In fact, if this could be 
done, the system just given might be taken for one of the 
systems of seven triads. With this system we might (of the 
systems of seven triads which contain the triad abd) combine 
either the system 

abd, acg, aef bee, bfg, dcf deg, 
or the system 

abd, acf, aeg, beg, bef, dee, dfg. 

But any one of the other abd systems would be found to 
contain a triad in common with the given abc system, and 
therefore cannot be made use of For instance, the system 
abd, aeg, aef, bef, beg, dee, dfg contains the triad beg in com- 
mon with the given abc system ; and whichever of the two 
proper abd systems we select to combine with the given abc 
system, it will be found that there is no ai^? system wliich does 
not contain some triad in common, either with the a6c system 
or with the abd system. 

The order of the letters in a triad has been thus far dis- 
regarded. There are some properties which depend upon 
considering the triads obtained by cyclical permutations of the 
three letters as identical, but distinct from the triads obtained 
by a permutation of two letters or inversion. Thus abc, bca, 
cab are to be considered as identical fw^lcrs^, but distinct from 
the triads acb, cba, bac, which are also identical inter se. I 
write down the system (equivalent, as far as the mere combi- 
nation of the letters is concerned, to the system at the com- 

* Communicated by the Author. 

0?i the Triadic Arra7igements of Seven and Fifteen Things, 51 

mencement of this paper) 

ade, afg, hdf, bgc, cdg, cef^ cha, 

derived, it is to be observed, from a pair of triads, ade, afg, 
by a cyclical permutation of the e^f, g, and by successively 
changing the a into b and c, the remaining triad of tlie system 
being the letters a, b, c taken in an inverse order. Let it be 
proposed to derive the system in the same manner from any 
other two triads of the system ; for instance, from the triads 
acb, ade. The process of derivation gives 

acb, ade, god, geb,fce,fbd,fga^-, 

which is, in fact, the original system. But attempt to derive 
the system from the two triads ebg, efc, the process of deriva- 
tion gives 

ebg, efc, dbf, dog, abc, agf, ade, 

which is not the original system, inasmuch as the triads dbf, 
dcg, abc, ag/ are inversions of the triads bdj] cdg, cba, afg of 
the original system. The point to be attended to, however, 
is, that both triads of the pair dbf, dcg, or of the pair abc, agf, 
are inversions of the triads of the corresponding pair in the 
original system; the pair is either reproduced (as the pair efc, 
dbf), or there is an inversion of both triads. Where there is 
no such inversion of the triads of a pair, the system may be 
said to be properly reproduced ; and where there is inversion 
of the triads of one or more pairs, to be improperly reproduced. 
There is no difficulty in seeing that the system is properly 
reproduced from a pair of triads containing in common any 
one of the letters a, b, c or d, and improperly reproduced from 
pairs of triads containing in common any one of the letters d, 
e ox f. It is owing to the reproduction, proper or improper, 
of the system from any pair of duads that it is possible to 
form a system of " octaves " analogous to the quaternions of 
Sir William Hamilton; the impossibility of a corresponding 
system of fifteen imaginary quantities arises from the circum- 
stance of there being always, in whatever manner the system 
of triads is formed, an inversion of a single triad of some one 
or more pairs of triads containing a letter in common. When 
the system is considered as successively derived from different 
pairs, the system is not according to the previous definition 
reproduced either properly or improperly. A system of triads 
having the necessary properties with respect to the mere com- 
bination of the letters (viz. that «/37 and aSs being any two 
triads having a letter in common, there shall be triads such 

* The order of the letters/, g is selected so as to reproduce the original 
system 30 far as the mere combination cf the letters is concerned. 


52 On the Triadic Arrangements of Seven and Fifteen Tilings. 

as ^3S, ^yr, and »i/3f, rjyS) may easily be found ; the system to 
be presently given of the triads of fifteen things would answer 
the purpose. And so would many other systems. 

Drojiping the consideration of the order of the letters which 
form a triad, I pass to the case of a system of fifteen letters, 
o, b, c, d, e,f, gy h^ i,j, Ic, /, m, ?/, o. It is possible in this 
case, not only to form systems of thirty-five triads containing 
every possible duad, but this can be done in such manner that 
the system of thirty-five triads can be arranged in seven systems 
of five triads, each of these systems containing the fifteen let- 
ters*. My solution is obtained by a process of derivation 
from the arrangements ab . cf. dg ,eli and ab . cd . ef.g/i as 
follows; viz. the triads are 

iab jac kaf 


mag nae oah 

icf JP ^''^c 


mch ncd ocg 

idg jde kdh 


mbd ngf ofd 

ieh jlig kge 


rafe nhb obe 

and a system formed with 

iji /< 

■, /, 7/?, 7?, 0, which are then 

arranged — 

klo ino jmo 


jln ijk kmn 

iab jac lad 


kaf mag oah 

nod mdb kbc 


mch Ice icf 

mef keg ieh 


obe ofd jde 

jgli Ihf nfg 


idg nhb Ibg 

an arrangement, which, it may be remarked, contains eight 
different systems (such as have been considered in the former 
part of this paper) of seven letters ; viz. of the letters /, j, k, 
I, ?«, n, o; and of seveii other sevens, such as ?,j, k, a, b,c,f. 
The theory of the arrangement seems to be worth further in- 

Assuming that the four hundred and fifty-five triads of 
fifteen things can be arranged in thirteen systems of thirty-five 
triads, each system of thirty-five triads containing every pos- 
sible duad, it seems natural to inquire whether the thirteen 
systems can be obtained from any one of them by cyclical per- 
mutations of thirteen letters. This is, I think, impossible. 
For let the cyclical permutation be of the letters ff, i, c, d, e^j\ 

* The problem was proposed by Mr. Kirkman, and has, to my knowledge, 
excited some attention in the form " To make a school of fifteen young 
ladies walk together in threes every day for a week so that each two may 
walk together." It will be seen from the text that I am uncertain as to 
the existence cf a solution to the further problem suggested by Mr. 
Sylvester, " to make the school walk every week in the quarter so that 
each three may walk together." 

Prof. Thomson on some remarkable effects of Lightning. 53 

5", /i, /,y, ^j /, m. Considtr separately the triads which conlain 
tlie letter n and the letter o ; neither of these systems of triads 
contains the letter, whatever it is, which forms a triad with n 
and o. Hence, omitting the letters ?/, o, we have twodillerent 
sets, each of them of six duads, and composed of the same 
twelve letters. And each of these systems of tluads ought, by 
the cyclical permutation in question, to produce the whole 
system of the seventy-eight duads of the thirteen letters. 
Hence arranging the duads of the thirteen letters in the form 

ah .he . C(l . de . cf .fg .gh . hi . ij .jk . kl . Im . ma 
ac .hd .ce . df, eg .fh . gi . hj . ik .jl . km . la . mh 
ad . he . cf. dg . eh .fi . gj .hk . il .jm . ka . Ih . vie 
ae .hf . eg . dh . ei .fj . gk . hi . im .ja . kh . Ic . md 
af . hg . ch . di . ej .fk . gl . hm . ia .jb , ke . Id . me 
ag . hh . ci . dj . ek .fl . gm . ha . ih .jc . kd . le . mf 
and consequently the duads of each set ought to be situated 
one duad in each line. Suppose the sets of duads are com- 
posed of the letters «, 6, c, r/, e^f g, h, i,j, k, /, it does not 
appear that there is any set of six duads composed of these 
letters, and situated one duad in each line, other than the 
single set al, hk, cj, di, eh,fg; and the same being the case 
for any twelve letters out of the thirteen, the derivation of the 
thirteen systems of thirty-five triads by means of the cyclical 
permutations of thirteen letters is impossible. And there does 
not seem to be any obvious rule for the derivation of the thir- 
teen systems from any one of them, or any prima facie reason 
for believing that the thirteen systems do really exist, it having 
been already shown that such systems do not exist in the case 
of seven things. 
2 Stone Buildings, June 14, 1850. 

V. On some remarkable effects of Lightiiifig, observed in a 
Farm-house near Moniemail, near Cupar-Fife. Communi- 
cated by William Thoi'mson, Esq., M.A., Fellow of St. 
Peter's College, Cambridge, and Professor of Natural Phi- 
losophy in the Universitij of Glasgow*. 

THE following is an extract from a letter, addressed last 
autumn to me, by the Rev. Mr. Leitch, minister of 
Moniemail parish : — 

" Moniemail Manse, Cupar-Fife, 
August 26, 1849. 

" * * We were visited on the 11th inst. with a violent 
thunder-storm, which did considerable damage to a farm- 
* Read before the Philosophical Society of Glasgow, Dec. 5, 1849. 

54- Prof. Thomson on some remarkable effects of Lightning. 

liouse in my immediate neighbourhood. I called shortly 
afterwards and brought away the wires and the paper which 
I enclose. * * 

" I have some difficulty in accounting for the appeai'ance of 
the wires. You will observe that f hey have been partially fused ; 
and when I got them first, they adhered closely to one another. 
You will find that the flat sides exactly fit. They were both 
attached to one crank, and ran parallel to one another. The 
question is, how were they attracted so powerfully as to be 
compressed together? * -'= 

" You will observe that the paper is discoloured. This 
lias been done, not by scorching, but by having some sub- 
stance deposited on it. There was painted 'wood also dis- 
coloured, on which the stratum was much thicker. It could 
easily be rubbed off, when you saw the paint quite fresh be- 
neath. * * 

" The farmer showed me a probang which hung on a , 
nail. The handle only was left. The rest, consisting of a 
twisted cane, had entirely disappeared. By minute examina- 
tion 1 found a small fragment which was not burnt but broken 

[The copper wires, and the stained paper enclosed with 
Mr. Leitcii's letter, were laid before the Society.] 

The remarkable effects of lightning described by Mr. 
Leitch, are all extremely interesting. Those with reference 
to the copper wires are quite out of the common class of 
electrical phaenomena ; nothing of the kind having, so far as 
I am aware, been observed previously, either as resulting 
from natural discharges, or in experiments on electricity. It 
is not improbable that they are due to the electro-magnetic 
attraction which must have subsisted between the two wires 
during the discharge, it being a well-known fact that adja- 
cent wires, with currents of electricity in similar directions 
along them, attract one another. It may certainly be doubted 
whether the inappreciably short time occupied by the elec- 
trical discharge could have been sufficient to allow the wires, 
after having been drawn into contact, to be pressed with 
sufficient force to make them adhere together and to produce 
the remarkable impressions which they still retain. On the 
other hand, the electro-magnetic force must have been very 
considerable, since the currents in the wires were strong 
enough nearly to melt them ; and, since they appear to have 
been softened, if not partially fused, the flattening and re- 
markable impressions might readily have been produced by 
even a slight force subsisting after the wires came in contact. 

Prof. Thomson on some remarkable effects of higlitning. 55 

I'he circumstances with reference to the probang, de- 
scribed by Mr. Leitch, alford a r...narkable illustration of 
the well-known fact, that an electrical discharge, when effected 
through the substance of a non-cotiducting (that is to say, a 
jjoxiocr/idhj resisting) solid, shatters it without producing any 
considerable elevation of its temperature, not leaving any 
marks of combustion, if it be of an ordi. M'y combustible ma- 
terial such as wood. 

Dr. Robert Thomson, at my request, kindly undertook to 
examine the paper removed from the wall of the farm-house, 
and enclosed with his letter to me by Mr. Leitch, so as if 
possible, by the application of chemical tests, to discover the 
staining substance deposited on its surface. Mr. Leitch, in 
his letter, had suggested that it would be worth while to try 
whether this case is an example of the deposition of sulphur, 
which Fusinieri believed he had discovered in similar circum- 
stances. Accordingly tests for sulphur were applied, but 
with entirely negative results. Stains presenting a similar 
appearance had been sometimes observed on paper in the 
neighbourhood of copper wires, through which powerful 
discharges in experiments with the hydro-electric machine 
had been passed ; and from this it was suggested that the 
staining substance might have come from the bell-wires. Tests 
for copper were accordingly applied, and the results were most 
satisfactory. The front of the paper was scraped in different 
places, so as to remove some of the pigment in powder, 
and portions of the powder from the stained and from the not 
stained parts were separately examined. The presence of 
black oxide of copper in the former was readily made manifest 
by the ordinary tests; in the latter no traces of copper could 
be discovered. The back of the paper presented a green 
tint, having been lorn from a wall which has probably been 
painted with Scheele's green ; and matter scraped away from 
any part of the back was found to contain copper. Since, 
however, the stains in front were manifestly superficial, the 
discoloration being entirely removed by scraping, and since 
there was no appearance whatever of staining at the back of 
the paper, nor of any effect of the electrical discharge, it was 
impossible to attribute the stains to copper produced from 
the Scheele's green on the wall below the paper. Dr. Thom- 
son, therefore, considered the most probable explanation to 
be, that the stains of black oxide of copper must have come 
from the bell-wire. To ascertain how far this explanation 
could be supported by the circumstances of the case, I wrote 
to Mr. Leitch asking him for further particulars, especially 

56 Prof. Thomson on some remarkable ejjects of Lightning. 

witli reference to this iK)int, and I received the following 
answer : — " Moniemail, Cupar-Fife, 

Nov. 30, 1849, 

" i: * I received yonr letter to-day, and immediately called 
at Ilall-hill, in the parish of Colessie, the farm-house which 
had been struck by the ]i<»htnin£r. ^- * 

" I find that Dr. Thomson's suggestion is fully borne out 
by the facts. I at first thought that the bell-wire did not 
run alojig the line of discoloration, but I now find that such 
was the case." * * 

[From a drawing and explanation which Mr. Leitch gives, 
it appears that the wire runs vertically along a corner of the 
room, fiom the floor, to about a yard from tlie ceiling, where 
it branches into two, connected with two cranks near one 
another and close to the ceiling.] 

" The efflorescence [the stains })reviously adverted to] was 
on each side of this perpendicular wire. In some places it 
extended more than a foot from the wire. The deposit 
seemed to vary in thickness according to the surface on which 
it was depositetl. 7"here was none on the plaster on the roof. 
It was thinnest upon the wall-paper, and thickest upon the 
wood facing of the door^''. This last exhibited various colours. 
On the thickest part it appeared quite black; where there 
was only a slight film, it was green or yellow. * * 

*' I may mention that the thunder-storm was that of the 
11th of August last. It passed over most of Scotland, and 
has rarely been surpassed for terrific grandeur, — at least 
beyond the tropics. It commenced about .9 o'clock p.m., 
and in the course of an hour it seemed to die away alto- 
gether. The peals became very faint, and the intervals be- 
tween the flashes and the reports very great, when all at once 
a terrific crashing peal was heard which did the damage. 
The storm ceased with this peal. 

" The electiicity must liave been conducted along the lead 
on the ridge of the house, and have diverged into thi-ee 
streams; one down through the roof, and the two others 
along the roof to the chimneys. One of these appears to 
have struck a large stone out from the chimney, and to have 
been conducted down the chimney to the kitchen, where it 
left traces upon the floor. It had been washed over before I 
saw it, but still the traces were visible on the Arbroath flags. 

* These remarkable facts are probably connected with the conducting 
powers of the different surfaces. The plaster on the roof is not so good a 
conductor as the wall-paper with its pigments; and the painted wood is 
probably a better conductor than either. — W. T. 

Iloyal Society, 57 

The stains were of a lighter tint than the stone, and the 
general ajipearance was as if a pail of some light-coloured 
fluid had been dashed over the floor, so as to prockice various 
distinct streams. All along the course of the discharge, and 
particularly in the neighbourhood of the bell-wires, there were 
small holes in the wall about an inch deep, like the marks 
that might be made by a finger in soft plaster. 

" Most of the windows were shattered, and all the frag- 
ments of glass were on the outside. I suppose this must be 
accounted for by the expansion of the air within the house. 

" The window-blind of the staircase, which was down at 
the time, was riddled, as if with small shot. The diameter 
of the space so riddled was about a foot. On minute exami- 
nation I found that the holes were not such as could readily 
be made by a pointed instrument or a pallet. They were 
angular, the cloth being torn along both the warp and the 

" The house was shattered from top to bottom. Two of the 
servant n)aids received a positive shock, but soon recovered. 
A strong smell of what was supposed to be sulphur, was per- 
ceived tlu'oughout the house, but particularly in the bed- 
room, in which the effects I described before took place." 

VI. Proceedings of Learned Societies. 


[Continued from vol. xxxvi. p. 549.] 

Feb. 7, " /^^ ^^^ development and homologies of the Molar Teeth 
1850. ^-^ of the Wart-Hogs (Phacocheerus), with illustrations 
of a System of Notation for the Teeth in the Class Mammalia." 
By Richard Owen, Esq., F.R.S. Src. 

Tlie author commences by a brief statement of the facts and con- 
elusions recorded in a paper by Sir Ev. Home on the dentition of 
the Shs j^thiopicus, in the Philosophical Transactions for 1799, 
p. 256 ; and gives the results of an examination of the original 
specimens described and figured by Home, and of other specimens 
showing earlier stages of dentition, which lead to the following 
conclusions as to the number, kinds, and mode of succession of 
the teeth in the genus Phacochcerits. The tooth answering to the 
first milk- molar and first premolar in the upper jaw, and those 
answering to the first and second milk-molars and corresponding- 
premolars in the lower jaw of the common Plog are not developed. 
Eight successive phases of development of the grinding teeth of the 
African Wart-hogs are described and expressed by the following 
notation : — 

58 Roijal Society, 

No. of grinding 
Phase. tot'tli. 

No. of grinding 
lasc. tootli. Kinds of topth. 

4—1. ' \ r/ 3, f/ 4, w/ 1 , w 2. 

II. ^"^ viz, 1^^ ^' J^ ^' 1^ ^' '" ^ ' "' -' ^" ^ 

.3-5 ' l/> 3, p 4, >« ] , m % m .'5. 

III. "'^~^ viz / '^ ■'^' ^ '^■' '" ^ ' "' ^' '" •^* 

l—l, ' 1^; 1, m 1, w? 2, ;« 3. 


IV. viz. p 4, m 1, ?« 2, w 3. 



4-4 . f ;^ 3, w 4, m 2, wt 3. 

VIZ. < -^ . ' ~ - 

3-3 I;' 4, 

^ I. ■ viz. /> 4, ?« 2, m 3. 

VII. ?::^ viz. »4, w3. 

VIII. ^"^ viz. m 3. 

The.'^e observations prove that, contrary to the opinion of Home 
and Cuvier, the Wart-hogs have deciduous teeth, succeeded verti- 
cally by premolar teeth; in the Pliacochcerus jEliani, at least, 
three deciduous teeth are, in some individuals, succeeded by as 
many premolar teeth ; and, as a general rule, two deciduous teeth 
are displaced vertically by two premolars. The first true molar is 
remarkable for its unusually early development, which is followed 
by an unusually early abrasion and expulsion, when its place is ob- 
literated by the second true molar being pushed forwards into con- 
tact with the last premolar. This tooth is as remarkable for its 
l;)ngevity, and remains after the wearing away and shedding of the 
second true mylar, when the last true molar advances into contact 
with the last premolar, and the place of both the previously inter- 
vening true molars is obliterated. This unusual order of shedding 
of the molar teetli has given rise to the idea of the last large and 
complex true molar of the Phacochterns being the homologue of 
both the last and penultimate grinders of the common Hog, which 
the author's observations refute ; and he, also, is able to point out, 
by re-examination of the original specimen figured by Home in the 
Phil. Trans., the source of the erroneous idea that the common Hog 
had an additional true molar behind the large one symbolised by 
m 3, in the author's system of dental notation. 

The nature and signification of the symbols proposed are ex- 
plained and illustrated by a series of drawings. One of the fruits 
of the determination of the homology of a part is the power of gi- 
ving it a name, and signifying it by a symbol applicable co-exten- 
sively with such homology. The linnts are shown within which 
the homologies of individual teeth can be determined : they present 

Royal Society. 59 

the requisite constancy of character in a large proportion of the 
class Mammalia. Certain members of tiiis class, e.g. the order 
Bruta and the Cetncea vera, have teeth too numerous and alike in 
form and mode of development to admit of being determined indi- 
vidually from species to species. Such mammalia have but one set 
of teeth, and the author proposes to call them ' Monophyodonts.' 
On the other hand, tlie orders Marsupialia, hisecfivora, Rodentiu, 
Knminantia, Pachj/dermnta, Cai-nivora, Cheiroptera, Quadrwnana 
and Bimana have two sets of teeth, and might be called collectively, 
' Diphyodonts.' Of the permanent teeth of this division of mam- 
malia, some succeed tlie deciduous teeth vertically, others come into 
place behind one-another in horizontal succession. The ' incisors' 
are determined by a character of relative position to the jaws and 
to each other : so likewise the ' canines.' The remaining teeth are 
divided into those which are developed in vertical relation to the 
deciduous molars, and push them out, and those that have not such 
relation, but follow each other horizontally: the term 'molar' is re- 
stricted by the author to these latter teeth, and that of 'premolar' 
to the former ones, which are always anterior to the molars. There 
is a remarkable degree of constancy in the number of these different 
kinds of teeth ; in the placental Diphyodonts, e. g. the ' incisors ' 

3 — 3 
never exceed -7, — -x, i. e. 3 on each side of both jaws, the ' ca- 
3 — 3 ^ 

Y \ 4 4. 3 3 

nines' \ 7> t'le premolars ^ ^ , the molars „_„ , =44 ; and this 

the author regards as the typical formula of dentition in the great 
proportion of the mammalian class above defined. It was rarely 
departed from by the primaeval sjiecies that have become extinct, 
and is modified chiefly by defect or loss of certain teeth in tlie ex- 
isting species. When the grinders are below the typical number, 
the missing molars are taken from the back part of their series, and 
the premolars from the fore part of theirs : the most constant teeth 
being the fourth premolar and first true molar ; these are always 
determinable, whatever be their form, by the relation to them of the 
last tooth of the deciduous series. Thus determined, the homo- 
logies of the other grinders are ascertained by counting the molars 
from the first backwards, 1, 2, 3 ; and the premolars from the last 
forwards, 4, 3, 2, 1. The symbols are made by adding the initial m 
to the numljers of the molar teeth, and the initial 77 to those of the 
premolar teeth. The author concludes by pointing out the advan- 
tages of this system of anatomical notation. 

2. " Description of the Hydrostatic Log." By the Rev. E. L. 
Berthon, M.A. Communicated by Sir Francis Beaufort, F.K.S. 
&c., on the part of tlie Lords Commissioners of the Admiralty. 

The object of this invention is to obtain a register of the speed 
of ships, by a column of mercury, in such a manner that the height 
of the column shall depend upon the velocity alone, and not be 
affected by any disturbing causes, such as alteration of draught of 
water, pitching and rolling, &'C. 

The principle embraces that of Pilot's tube, inasmuch as the 

GO Royal Societij. 

force of the resistance due to the velocity is communicated throuj^h 
a small \n\)o projectini^ into tlie water below tlie bt)ttom of tiic shi]): 
this force, acting upvsards, compresses a jjortion of enclosed air in a 
small cylinder, which air connnunicating by means of a little pipe 
with the bulb of a glass tube — bent like a common barometer — 
raises the mercury in the tube, by depressing it in the bulb. 

But as any single column of water and air thus acting upon tiie 
surface of the mercury in the hidb nloitc must depend not only upon 
the resistance due to the velocity, but also upon the distance of the 
cyinider from the water-line, w hicli distance or height varies w ith 
every sea, and alters more permanently as the draught of water 
changes, a compensation was necessary ; and the inventor has found 
one, which he considers perfect for all these variations, by applying 
(I second coluDui of water and air to press upon the other snifacc of 
the inercurij, viz. that in the glass tube. This second column is 
])recisely like the first as regards the pipe and cylinder, and commu- 
nicates with the sea by an aperture or apertures, presented in sucii 
a direction that velocity does not produce any increase of pressure. 
'Jims the mercury in the indicator is placed between two columns 
of water antl air, which are (dways equal to each other in length, and 
the mercury rises according to the difference between the pressures 
upon its two surfaces, the result of resistance or velocity alone. 

The air-pipes may be conducted in any direction, and the indi- 
cator, Avhicli swings upon gimbals, may be placed in any part of 
the ship. The two water-pipes are conducted into one tube in the 
bottom of the ship, divided into two separate chambers for the dif- 
ferent forces. 

In addition to the speed, the true course or leeway of the vessel 
is indicated upon a horizontal segment divided into degrees, over 
which a needle is moved by a rod connected with the above-men- 
tioned double tube ; and the whole is kept continually in the true 
direction of the ship's motion by a float or vane attached to the 
lower end of the tube in the water. 

Feb. II'. — " Supplementary Observations on the Structure of the 
Belemnite and Belemnoteuthis." By Gideon Algernon Mantell, Esq., 
LL.D., F.K.S., Vice-President of the Geological Society, &c. 

In this communication the author describes his recent investiga- 
tions on the structure of the two genera of fossil Cephalopoda, w hose 
remains occur so abundantly in the Oxford clay of Wiltshire, 
namely, the Belemnite and Belenmoteuthis, as supplementary to his 
memoir on the same subject, published in the Phil. Trans. IStS. In 
that paper evidence was adduced to show the correctness of the 
opinion of the late Mr. Channing Pierce as to the generic distinction 
of these two extinct forms of Cephalopoda. 

As however several eminent naturalists had expressed doubts as 
to some of the opinions advanced by the author in his former memoir, 
figures and descriptions are given in the present notice, of beautiful 
and instructive specimens lately discovered in Wiltshire, and which 
he conceives establish his previous conclusions. Dr. Mantell then 
states as the result of his examination of several hundred examples. 

Royal Society. 61 

tliat our knowledge of the organization of the animal of the Beleni- 
nite is at present limited to the following parts, viz. — 

1. An external Capsule or periostracum wliicli invested the osse- 
let or sepiostaire, and extending upwards, constituted the external 
sheath of the receptacle. 

2. The Osselet, characterized by its fibrous radiated structure, 
terminating distally in a solid rostrum or guard, having an alveolus, 
or conical hollow, to receive the ajiical portion of the chambered 
phragmocone ; and expanding proximally into a thin cup, which 
became conHuent with the capsule, and formed the receptacle for 
the viscera. 

3. The Phragmocone, or chambered, siphunculated, internal shell ; 
the apex of whicli occupied the alveolus of the guard, and the upper 
part constituted a capacious chamber, from the basilar margin of 
which proceeded two long, flat, testaceous processes. 

These structures comprise all that are at present known of the 
animal to which the fossil commonly called " The Belemnite" 

Of the Belemnoteuthis, the fossil cephalopod which Prof. Owen 
regards as identical with the Belemnite, many examples of the body 
with eight uncinated arms, and a pair of long tentacula, having an 
ink-bag and pallial fins, have been discovered. The osselet of this 
animal, like that of the Belemnite, has a fibro-radiated structure, 
investing a conical chambered shell ; but this organ, for reasons 
fully detailed in the memoir, the author considers could never have 
been contained within the alveolus of a Belemnite; the soft parts 
of the animal of the Belemnite are therefore wholly unknown. 

Many beautiful specimens of Belemnites and Belemnoteuthis were 
exhibited by Dr. Mantell to the Society, in proof of the statements 
contained in the memoir. 

2. "On the Pelorosaurus ; an undescribed gigantic terrestrial 
reptile, whose remains are associated with those of the Iguanodon 
and other Saurians, in the Strata of Tilgate Forest." By Gideon 
Algernon Mantell, Esq., LL.D., F.R.S., Vice-President of the Geo- 
logical Society, &c. 

The author had for a long while entertained the idea, that among 
the remains of colossal reptiles obtained from the VVealden strata, 
there were indications of several genera of terrestrial saurians, 
besides those established by himself and other geologists. The re- 
cent discovery of an enormous arm- bone, or humerus, of an unde- 
scribed reptile of the crocodilian type, in a quarry of Tilgate Forest 
in Sussex, where Dr. Mantell had many years since collected nume- 
rous teeth and bones of the Iguanodon, Hylseosaurus, &c., and some 
remarkable vertebrae not referable to known genera, induced him to 
embody in the present communication the facts which his late re- 
searches have brought to light 

The humerus above-mentioned was found imbedded in sandstone, 
by Mr. Peter Fuller of Lewes, at about 20 feet below the surface ; 
it presents the usual mineralized condition of the fossil bones from 
the arenaceous strata of the Wealden. It is four and a half feet in 

G2 Royal Socicfj/. 

length, iiiitl tlie circuinferonce of its distal extremity is ;J2 inches I It 
has a lui'diillai y cavity [i inclies in ilianioter, which at once separates it 
from the C'etiosaurus anil uther supposed marine saurians, while its 
form and proportions distinguish it from the humerus of the Tgua- 
nodon, Hyla>osaurus. and Megalosaurns. It approaciies most nearly 
to the Crocodilians, but [lossesses characters distinct from any known 
fossil genus. Its size is stupenilous, far sur))assing that of the cor- 
responding bone even of the gigantic Iguanodon ; and the name of 
Pi'ldrosdiirus (fiom iTt\u)p pc/or, monster) is therei'ore proposed 
for the genus, with the specific term Com/htari, in honour of the 
jiala?ontological labours oithe Dean of LlancUiff. 

No bones have been found in such contiguity with this humerus, 
as to render it certain that they belonged to the same gigantic rep- 
tile ; but several very large caudal vertebrre of peculiar characters, 
colU'Cted from the same quarry, are probably referable to the Pelo- 
rosaurus; these, together with some distal caudals which belong to 
the same type, are figured and described by the author. 

Certain femora and other bones from the oolite of Oxfordshire, 
in the collection of the Dean of Westminster, at Oxford, are men- 
tioned as possessing characters more allied to those of tiie Pelo- 
rosaurus, or to some unknown terrestrial saurian, than to the Ce- 
tiosaurus, with which they have been confounded. 

As to the magnitude of the animal to which the humerus belonged. 
Dr. Mantell, while disclaiming the idea of arriving at any certain 
conclusions from a single bone, states that in a (iavial 18 feet 
long, the humerus is 1 foot in length ; ^. e. one-eighteenth part of 
the length of the animal, from the end of the muzzle to the tip of 
the tail. According to these admeasurements the Pelorosaurus would 
be 81 feet long, and its body "20 feet in circumference. But if we 
assume the length and number of the vertebrse as the scale, we 
should have a reptile of relatively abbreviated proportions ; even in 
this case, however, the original creature would far surpass in mag- 
nitude the most colossal of reptilian forms. 

In conclusion, Dr. Mantell comments on the probable physical 
conditions of the countries inhabited by the terrestrial reptiles of the 
secondary ages of geology. These highly-organized colossal land 
saurians appear to have occupied the same position in those ancient 
faunas as the large mammalia in those of modern times. The trees 
and plants whose remains are associated with the fossil bones, mani- 
fest, by their close affinity to living species, that the islands or con- 
tinents on which they grew possessed as pure an atmosphere, as 
high a temperature, and as unclouded skies as those of our tropical 
climes. There are therefore no legitimate grounds for the hypo- 
thesis in which some physiologists have indulged, that during the 
" Age of Reptiles " the earth was in the state of a half-finished 
planet, and its atmosphere too heavy, from an excess of carbon, for 
the respiration of warm-blooded animals. Such an opinion can only 
have originated from a partial view^ of all the phenomena which 
these problems embrace, for there is as great a discrepancy between 
the existing faunas of different regions, as in the extinct groups of 
animals and plants which geological researches have revealed. 

lioyaL Society. 63 

The memoir was illustrated by miiuerous drawings, a?id tlie gi- 
gantic luiiuerus of the Pelorosaurus and other bones were jjlaced 
before the Society. 

Feb. 21. — " On the Extension of the Principle of Fennat's The- 
orem of the Polygonal Numbers to the higher orders of series whose 
ultimate differences are constant. With a new Theorem proposed, 
applicable to all the Orders." By Sir Frederick Pollock, Lord Chief 
Baron, F.K.S. 

The object of this paper professes to be to ascertain whether the 
principle of Fermat's theorem of the polygonal numbers may not be 
extended to all orders of series whose ultimate differences are con- 
stant. The polygonal numbers are all of the quadratic form, and 
they have (according to Fermat's theorem) this proj)erty, that every 
number is the sum of not exceeding, 3 terms of the triangular num- 
bers, \ of the square numbers, 5 of the pentagonal numbers, &c. 

It is stated in this paper that the series of the odd squares 1,9, 25, 
49, &c. has a similar property, and that every number is the sum of 
not exceeding 10 odd squares. It is also stated, that a series con- 
sisting of the 1st and every succeeding 3rd term of the triangular 
series, viz. 1,10, 28, 3.5, &c., has a similar pi-operty ; and that every 
number is the sum of not exceeding 1 1 terms of this last series, and 
that this naay be easily proved [it was proved in a former paper by 
the same author]. The term "Notation-limit" is applied to the num- 
ber which denotes the largest number of terms of a series necessary 
to express any number; and the writer states that 5, 7, 9, 13, 21 are 
respectively the notation-limits of the tetrahedral numbers, the octo- 
hedral, the cubical, theeicosahedral and the dodecahedral numbers; 
that 19 is the notation-limit of the series of the 4th powers; that 
11 is the notation-limit of the series of the triangular numbers 
.squared, viz. 1, 9, 36, 100, &'C., and 31 the notation-limit of the series 
1, 28, 153, &c. (the sum of the odd cubes), whose general expression 
is 2m* — n'^. 

The paper next contains an extension of the theorem 8?^-|-3 = 3 odd 
squares, which was proved by Legendre in his Theorie des Nombres ; 
every odd square equals 8 times a triangular No.+ l ; the theorem 
therefore is — 8 times any term in the figurate series (1, 2, 3, 4, &c. ..) 
-f 3 = 3 terms of a series consisting of the next series, viz. (1, 3, 6, 
10 . . <ic.), multiplied by 8 v.ith 1 prefixed, and also added to each 
term. But it is stated that this theorem may be much extended; for 
this is not only true of any two consecutive series, but generally if F^,. 
represent any figurate number of the x'-^ order, and F^ any figurate 
number of the ?/*'' order, whether y be greater or less than x, 

8F,-|-3 = 3, or (3 + 8), or (3 + 2 .8), or . . . (3 + »8), &c., 

terms of a series whose general expression is 8Fj, + l ; and still fur- 
ther (provided j^ be greater than 2) — 

^F^ + 3 = 3, or (3+7?), or (3 + 2p), or (3 + «jo), 

terms of a series whose general expression is />Fj, + 1, and vice versa. 
The author concludes from these considerations, that probably 

64' Tloyal Societi/. 

there are many theorems M-hich are common to all the orders. The 

following tlicoreiii is then proposed as having that character. 
If tlie terms of a stnies be 

1, or {\+n)\ (I +»)'» (1 +^0' . . . .S-c. (1 +«)", 

the 1st (p + \) terms of (1 +«/^' 

the Ut (j)+\) terms of (1 -\-ny'^''- 

the 1st (jo + l) terms of (1 +«)''"^^ 

+ &c. &c. 

(ify> and ii bo botli not less tlian 1), any number will be the sum of 
not exceeding (y>;/ + 1 ) terms of the series; in other words, j9n-fl 
is the notation-limit of this series. 

It is manifest that this series is of such a form, that by varying 
11 and/>, it is capable of expressing every possible arithmetical series, 
also every possible geometrical series (each having 1 for the first 
term) ; it will also express all the intermediate series of the success- 
ive orders (to an indelinite extent), which exist between and con- 
nect together by a regular gradation (as is well known) any such 
arithmetical series witli a geometric series, whose common ratio is 
the 2nd term of both series. The theorem may be statedwithout 
the series thus : — 

If any geometric series (having ] for its first term) and (1+w) 
for its common ratio, be stayed at the {p-\-\)i\i term and discon- 
tinued as -A geometric series, but be continued from that term as an 
arithmetic series of the pth order, by forming it with the pth differ- 
ence as the constant difference, and the other differences (which 

will be X, x", .r^ &c x''). The resulting series will be 

the series stated in the theorem above, and any number may be 
formed by not exceeding (pn+l) terms, that is (p?i+i) will be 
the notation-limitof the series; ify> becomes indefinitely great, the 
limit of tlie series is a geometrical series, and it would become capa- 
ble of expressing any number according to a system of notation 
whose base or local value would be (1 + n). 

The proof of the theorem seems to depend upon this, that the no- 
tation-limit assigned by the theorem is actually the notation-limit 
of all the geometric terms and one more, at least, while the geometric 
terms alone fix the law of the series and ascertain its elements (tliat 
is, the first term and the successive differences) ; and as the com- 
binations necessary to enable the series to fulfill its law, and carry 
on the notation that belongs to it, are regulated by the series next 
below it, viz. by the first rank of differences, while the supply of 
new combinations (as the series advances and the number of terms 
that may be used increases) is indicated by even a higher series than 
itself, the new combinations are always greater, and at length inde- 
finitely greater, than the number required. If therefore within the 
range of those terms that ascertain and fix the law of the series the 
law of its notation-limit can be obeyed, it must always {a fortiori) 
he obeyed as the series proceeds to a greater number of terras and 
to a variety of combinations increasing in a liigher ratio ; and the 

Rqi/al Society. G5 

series will furnish the niunbers refjuisite to carry on the notation by 
the new and more ntinieroiis combinations which nuist of necessity 
be of the same nnmerical kind with tliose which iiavc; jireceded them. 
It is shown at length, that the new combinations, as tlie series ad- 
vances, do actually increase in an increasing proportion compared 
with the numbers required. 

2. " Experiments on the section of the Glossopharyngeal and 
Hypoglossal Nerves of the Frog, and Oljservations of the altera- 
tions produced thereby in the Structure of their primitive fibres." 
Bv Augustus Waller, M.D. Communicated by Professor Owen, 
FJl.S. See. 

After describing the natural structure of tlie tubular fibres of the 
nerves, the author states the results which he observed to follow 
the section of the nerves of the frog's tongue. To this organ two 
principal pairs of nerves are distributed ; one of these, issuing from 
the cranium along witli tlie pueumogastric and distributed to the 
fungiform papilla}, is regarded as the glossopliaryngeal ; the other, 
arising from the anterior part of the spinal cord, and passing through 
the first intervertebral foramen, the author (following Burdach) 
names the hypoglossal. Section of the glossopharyngeal nerves 
does not cause any pei'ceptible loss of motion or of common sensa- 
tion, and this fact, together with its distribution to the fungiform 
papillae, leads the author to consider this nerve as the nerve of 
tasting. On tlie other hand, when the hypoglossal nerves are 
divided, the tongue is no longer sensible to mechanical irritation, 
and its motions are entirely abolished. Simultaneous division of 
the right and left glossopharyngeal nerves is followed by the death 
of the animal in a few days, and the same eft'ect ensues alter division 
of both hypoglossals. This result, which takes place more speedily 
in summer than in winter, the author is disposed to ascribe to a 
disturbance of the mechanical process of respiration, in which, as is 
well known, the muscles of the frog's mouth and tongue take a 
large share. 

To ascertain the changes which take place in the nerve-fibres 
after division of the trunks to which they belong, the operation was 
confined to the nerve of one ^ide only, and tlie fibres of the unin- 
jured nerve of the other side served for comparison. These changes 
ensue more speedily, and go on more rapidly in summer than in 
winter, commencing usually in about five days. The pulp contained 
in the tubular nerve-fibres, originally transparent, becomes turbid, 
as if it underwent a sort of coagulation, and is soon converted into 
very fine granules, 2:»artly aggregated into small clumps, and partly 
scattered within the tubular membrane. These granules are at first 
abundant, and render the nerve-fibre remarkably opaque ; but in pro- 
cess of time they diminish in number, and, together with the inclosing 
membrane, at length disappear, so that at last the finest ramifications 
of the nerves which go to the papillaj, or those going to the muscular 
fibres of the tongue (according to the nerve operated on), are 
altogether lost to view, in consequence of the destruction and eva- 

P/iU. Mag. S. 3. Vol. 37. No. 247. Jidj/ 1850. F 

66 Hoyal Sociclij. 

nescence of their elementary fibres. Tlie disorganization begins at 
the extremities of the fibres, and gradually extends upwards in the 
branches ami trunk of the nerve. The other tissues of the tongue 
remain luialteretl. Wlun tlie cut ends of the nerve are allowed to 
reunite, the process of disorganization is arrested, and the nervous 
fibres are restored to their natural condition. The author ascribes 
the disorganization and final absorption of the nerve-fibres to an 
arrestment of tiieir nutrition caused by interruption of the nervous 
current, and considers his experiments as atlbrding most unequivocal 
evidence of the dependence of the nutrition on the nervous power. 

Feb. 28. — " Sequel to a Paper on the reduction of the Thermo- 
metrical Observations made at the Apartments of the Royal Society, 
with an Appendix." By James Glaisher, Esq., F.R.S. 

The principal object of this paper is the connexion of the results 
deduced in a former paper from the observations at the Royal So- 
ciety's Apartments, with the observations at the Royal Observatory 
at Greenwich, in order to determine mean numerical values, and to 
establish the laws of periodic variation from this long series of obser- 
vations ; the two series of observations are here reduced to one and 
the same series. 

The observations at the Royal Society having been discontinued 
between the years 1781 and 1786, it was necessary to supply this 
link in the series, more particularly as these years were distinguished 
by very severe weather, and their omission would have a sensible 
effect on the results. The deficient observations have been supplied 
by a comparison of the observations which were made at Somerset 
House, with the observations during the corresponding years made 
by Mr. Barker at Lyndon in Rutlandshire, from 1771 to 1799, cor- 
rections being thus obtained for reducing the Lyndon observations 
to those at Somerset House. 

By a comparison of the temperature of the air at Somerset House 
and at the Royal Observatory for every month during the years 
1833 to 184-3, corrections necessary to be applied for reducing the 
mean values at the one place to those at the other, are deduced. 

Thus the results of the observations at Somerset House are re- 
duced to those at the Royal Observatory, and a table is given showing 
the mean temperature at the latter place of each month in every year 
from 1771 to 1849 inclusive. By taking the means of the several 
columns in this table, the mean temperature of each month is deduced 
from all the observations. From these mean monthly temperatures 
a table is constructed showing the excess of the mean monthly tem- 
perature at Greenwich' for each year, above the temperature of the 
month deduced from all the years. 

Tables are next given showing the mean temperature in quarterly 
periods for the year, and for successive groups of years at the Royal 
Observatory at Greenwich, from the year 1771 to 184'9; and the 
excess of the quarterly and yearly mean tem))eratures in every year, 
and for groups of years, above the means from all the years. The 
author remarks that the numbers in these tables do not at all confirm 
the idea tliat a hot summer is either preceded or followed by a cold 

Royal Sociely. 67 

winter, or vice versa; but on the coiitrarj' it would appear that any 
hot or cold period has been mostly accompanied by weather of the 
same character, and instances are cited in support of this conclusion. 

Tables are also given, based upon the readings of the self-registering 
thermometers, exhibiting the extreme readings at Somerset House 
and at the Royal Observatory. 

Incidentally the author goes into an inquiry respecting the relative 
temperature of London and the country in its neighbourhood. From 
the observations made by Mr. Squire at Epping from 1821 to IS^S, 
and also from those at Lyndon, he concludes that the general fact 
of a higher winter temperature and lower summer temperature at 
the Royal Society's Apartments is satisfactorily proved, and that the 
same cause has been in operation at both seasons ; this cause he 
considers to be the vicinity of the river Thames to the place of ob- 
servation. With the view of showing the extent to which this cause 
operates, a table is given of the mean monthly temperature of the 
water of the Thames, and a comparison is made between the results 
of observations made on board the 'Dreadnought' Hospital Ship, at 
tlie height of 32 feet above the water, with simultaneous observa- 
tions at the Royal Observatory. From this comparison it is con- 
cluded, that at all seasons of the year the temperature at the ' Dread- 
nought' is above that at the Observatory during the night hours, 
arid that it is below during the mid-day hours only : at times of ex- 
treme temperature the effects of the water upon tlie temperature of 
the air is very great. 

The paper is accompanied by diagrams exhibiting to the eye, by 
means of coordinates, the numerical results given in the tables. 

2. " On the Communications between the Tympanum and Palate 
in the Crocodilian Reptiles." By Richard Owen, Esq., F.R.S. <S:c. 

After citing the descriptions by Cuvier, Kaup, Bronn, and De 
Blainville of the Eustachian tubes and the foramina in the base of 
the cranium of the recent and extinct Crocodiles, the author gives an 
account of the nerves, arteries, veins and air-tubes that traverse these 
different foramina, and thus determines the true position of the ca- 
rotid foramina and posterior nostrils in the Teleosauri and other 
fossil Crocodilia, which had been a matter of controversy amongst 
the authors cited. In the course of these researches the author dis- 
covered a distinct system of Eustachian canals superadded to the or- 
dinary lateral Eustachian tubes, wliich he describes as follows: — 

"From each tympanic cavity two passages are continued down- 
wards, one expands and unites with its fellow from the opposite side 
to form a median canal which passes from the basisphenoid to the 
suture between that and the basioccipital, where it terminates in the 
median canal continued to the orifice described by M. De Blainville " 
as the posterior nostril. The second passage leads from the floor of 
the tympanic cavity to a short canal which bends towards its fellow, 
expands into a sinus and divides : one branch descends and termi- 
nates in the small lateral foramen at the lower end of the suture be- 
tween the basioccipital and the basisphenoid : the other branch 
continues the course inwards and downwards until it meets its fellow 
at the median line of the basioccipital, and it forms the posterior 


68 Cambridge Philosophical Society. 

primary division of the common nunlian canal : tiiis soon joins tlie 
anterior division, and the common canal terminates at the median 
opening below. Membranous tubes are continued from the three 
osseous ones, and converge to terminate finally in the single Eusta- 
chian orifice on the soft palate behind the posterior nostril. The 
mucous membrane of the palate lines the various osseous canals 
above described, and is continued by them into the lining membrane 
of the tympanum." 

Witii regard to the homologies of the above described air-passages, 
the author states that the lateral canals answer to the simple Eusta- 
chian tubes of Lizards and .Mammals, and that the median canal, 
with its diehotomous divisions, is a sjjeciality i)eculiar to the Croco- 
dilian reptiles. 

The nu;moir was illustrated by nine drawings of the size of nature. 

[Continued from vol. xxxvi. p. 240.] 
March 11, 1850. — On the Numerical Calculation of a class of 
Definite Integrals and Infinite Series. By Professor Stokes. 

In a paper " On the Intensity of Light in the neighbourhood of a 
Caustic," printed in the sixth volume of the Cambridge Philosophical 
Transactions, Mr. Airy, the Astronomer Royal, has been led to con- 
sider the integral 

W = / CCS — (lo^ — miv)dw, 

and has tabulated it from >«= —4 to 7h= -f 4 by the method of qua- 
dratures. In a supplement to the same paper, j)rinted in the fifth 
part of the eighth volume, Mr. Airy has extended the table as far as 
?H^= + 5'G, by means of a series proceeding according to ascending 
powers of ?n. This series, though convergent for all values of m, 
however great, is extremely inconvenient for numerical calculation 
v.'hen m is large, and moreover gives no information as to the law of 
the progress of the function for large values of ?h. The author has 
obtained the following expression for the calculation of W for large, 
or even moderately large, positive values of m : 

W = 2(3/«)-^|Rcos U--\ + '&?.mU--\ |, 


T^^l— 1-5-7.11 1.5. 7. 11.13.17. 19. 23 _ 

1.2(72^)^^7 "" 

• «g— ^-"^ _ I .5. 7. 11.13. 17 

1.720 1.2.3(72^)3 ' 

When m is negative, and -{-mw is written for —miv in the integral 
W, so that in the altered form of the integral m is positive, there 

W=2-J(3mWs-^|l- '^-^ + 1-5.7.11 _ \ 
^ V I 1.72^ ].2(72f)^ J 

Royal Astronomical Societj/. 69 

By means of these expressions, \V may be calculated with great 
facility when m is at all large. The author has given a table of the 
roots of the equation W = 0, from the second to the fiftieth inclusively, 
calculated by a formula derived from the former of the above expres- 
sions. This formula was not sufficiently convergent to give the first 
root to more than three places of decimals ; but this root may be 
obtained more accurately from Mr. Airy's table. 

The method by which the author has treated the integral W ap- 
pears to be of very general application, and he has further exem- 
plified it by applying it to the infinite series 


H — + ...= - / cos (A' cos 9 )a9, 

22.42 22. 4'-. 6--^ ttJo ^ ^ 

which occurs in a great many physical investigations, as well as to 
the integral which occurs in investigating the diflfraction produced 
by a screen with a small circular aperture, placed in front of the 
object-glass of a telescope through which a luminous point is viewed. 

[Continued from vol.xxxvi. p. 477-] 

Jan. 11, 1850. — An account of some Improvements in a Speculum 
Grinding and Polishing Machine. By John Hippisley, F.R.A.S. 

" The machine, as far as regards the general action of two excen- 
tric pins, which transmit motion to the grinding and polishing tools, 
is similar in principle to that adopted by Lord Rosse, and other ma- 
chines previously in use. 

" The improvements consist in the arrangement of the parts so 
as to eflfect cheapness and facility in the construction, with general 
convenience in use, and especutUy in th.e manner in which the polish- 
ing tool is connected with the apparatus which gives it motion. 

"This connexion is made by a ball and socket-joint of a novel 
construction, w-hich, while it transmits a perfectly equable motion, 
without jerks or irregularities, to the polisher, and leaves it free also 
to revolve about its own ceritre, as the friction between it and the spe- 
culum may direct, facilitates the application of counterpoise weights, 
so as to counterbalance in any required degree the weight of the 
polisher, especially in the very last period of the polishing. 

" A polisher of considerable lightness has justly been deemed in- 
dispensable, and for this purpose wood has been used instead of metal 
in its construction. This material is, however, obviously liable to 
unsymmetrical alteration of figure, from unequal expansion and con- 
traction bj' moisture and heat. 

" Nor does it, it is submitted, adequately fulfill the condition re- 
quired, namely, that of sufficiently removing jn-essure from the spe- 
culum. It appears almost demonstrable that the last finishing action 
of the polisher will be exerted with most advantage, to the perfection 
both of figure and polish, when it moves without any vertical pressure 
whatever. Those who are familiar with the adjustment of reflecting 
telescopes are aware that the slightest confinement or pressure on 
the speculum, when in its place in the telescope, is sufficient to im- 
pair its power of definition, in other words, to alter temporarily, in 

70 Roual Astronomical Society. 

some degree, however small, its figure. A pressure, certainly far 
less than that which a wooden polisher will exert, is capable of pro- 
ducing this injurious effect. 

" It is, then, to be expected, that when a speculum has been re- 
ceiving its final figure under any pressure, there will be some, 
however slight, recession from that figure when the pressure is re- 
moved ; and if so, the remedy obviously is to diminish successively , 
by counterpoises, the weight of the polisher as the figure and polish 
are advancing, till it ultimately moves, in giving the last finishing 
strokes, without any more pressure than the cohesion between the 
polished and sliding surfaces aft^ords. It may also be expected that 
the lustre and perfection of the polish itself will be enhanced, inas- 
much as the size of the abraded atoms will then be at their minimum, 
since they diminish in a direct ratio with the diminution of pressure 
by the abrading surface. 

" In the machine to which these observations refer, the pulley 
which drives one excentric rod is made to differ slightly in diameter 
from its fellow, with which it is connected by the endless band, 
Avhich gives motion to the other excentric rod ; so that the centre of 
the polisher, by their joint action, is constrained to describe curves, 
varying from nearly a straight line to ellipsoids having a minor axis 
equal to twice the thrust of the shorter excentric ; and the parabolic 
figure is attained bj^ the maintenance of a certain proportion, found 
experimentally, between the throws of these two excentrics. This 
])roportion, for a speculum having an aperture of one inch for each 
foot of focal length, and under the action of a polisher of the same 
dimensions as the speculum, is one-third of the diameter of the spe- 
culum for the longer, and one-seventh for the shorter thrust ; the 
figure of the speculum receding towards a spherical figure if that 
shorter thrust be diminished, or advancing to the hj-perbolic curva- 
ture if it be increased. 

" The counterpoises, then, it is suggested, should be added suc- 
cessively, and at those periods in the action of the machine when it 
may be considered that its tendency to give a i^arabolic figure is at 
its maximum ; that is, when, by the combined action of the excentric 
pins, the centre of the polisher is describing the widest ellipsoids on 
the speculum. A bent w^ire is so placed, as an index, on the excen- 
tric rod, that its point, traversing a scale fixed in any convenient 
position, shows the exact moment when these widest ellipsoids are 
being described : at those intervals the counterpoise-weights are 
successively added, so that the polisher may be considered to pass 
through complete cycles of its action under each alteration and dimi- 
nution of i:)ressure. 

"Attention to these conditions has, in specula finished by the 
machine, apparently been entirely successful, both in obtaining an 
exceeding fine polish, and a figure which does not sensibly deviate 
from the parabolic. 

" A nice attention to the quantity and purity of the water used in 
the polishing is also of much importance. A very convenient method, 
which, being- self-acting, requires no particular care during the pro- 
cess, is to fix a small vessel on the excentric rod, with a thread de- 

British Meteorological Societi/. 7 1 

pending from it, and so adjusted, that the single drop, which by the 
cajjilUiry and syphon action passes from the thread, shall, at the 
extreme thrust of the excentric rod, be deposited at the edge of the 
sjieculum. The quantity may be nicely regulated by the use of a 
smaller or larger thread ; and the water is secure from containing 
any gritty particle, being filtered in its passage through the thread. 
"The machine is of an easy and cheap construction, and intended 
to be worked by the foot acting on a treadle, or by any other con- 
venient motive power : the same lever apparatus which is used for 
counterpoising the polisher in finishing, being connected by a ver- 
tical rie:id bar with the ball and socket-joint of the tool, affords means 
for adding any required amount of pressure in the rough grinding 
process, and thus that tedious part of the operation is considerably 
accelerated. It is also adapted for figuring lenses of large dimen- 
sions, to which it ^vould impart, as well as to specula, surfaces ap- 
proaching nearly to those of parabolic, or other required geometric 
curvatures, and with the addition of another mandril, or more, re- 
ceiving rapid motion from the periphery of the fly-wheel, it has been 
used with great convenience for grinding and polishing lenses of the 
smallest dimensions." 

, We have to notice the recent formation of a Society for the advance- 
ment of Meteorological knowledge, " a branch of physical inquiry 
W'hich," as stated in the published Address, "requires the combined 
efforts of numerous observers, steadily following a well- concerted 
plan, employing the same class of instruments, and reducing their 
results in the same form. 

"Amongst the objects of this Society will be the reduction of 
observations and combination of results, as far as their funds will 
allow ; nevertheless it is to be hoped that the emulation which will 
naturally be excited amongst observers to sujiply observations pro- 
ducing the best results, will also induce them to reduce their own 
observations, as far as they may be able to do so. With the view 
of stimulating observers to perform this work, this Society will 
publish from time to time useful Tables to facilitate the reduction of 

" The Council fully trust, that whilst the establishment of the 
British Meteorological Society will be the means of diffusing through- 
out this country a philosophical spirit of inquiry, and of inducing a 
more general employment of trustworthy instruments, and the care- 
fully noting and submitting for comparison the observations thus 
made, it will also have a more extended influence. By facilitating 
a comparison of the observations of its own members with those 
made in other countries, meteorological phaenomena will be better 
traced, and thus eflfects more satisfactorily and surely referred to 
their true causes. A remarkable instance of the want of connecting 
observations has been so recently rendered obvious, that it may not 
be without its use briefly to refer to it here. In the ' American 
Traveller,' published at Boston on April 6, 1850, and recently re- 
ceived in this country, is a paper by W. Cranch Bond, Esq., of Cam- 

72 Inlelligcnce and Miscellaneous Articles. 

bridge, Ignited States, in wliicli he sponks of the groat atmospheric 
vave whieh was passing over I'^ngland from the 1st to the ISth day 
of February 1S49, the mean reading of the barometer during tliis 
interval of time being fully half an inch above its average value, and 
when the crest of the wave was over Greenwich, the reading of the 
barometer at the level of the sea was 30"y() inches. The base of 
the wave at this time seems to have been in extent just equal to the 
distance from England to America ; for on the same day that it com- 
pleted its i)assagc at Greenwich, it was first felt at Boston, and it 
was seventeen days passing over Boston, as it was with us. Its 
motion, therefore, must have been about 170 miles daily. The re- 
duced readings of the barometer during the time of the passage of 
the wave at Boston, and its extreme readings, were identical in value 
with those at (treenwich. At present we cannot follow this very 
remarkable heaping up of the air from the want of observations at 
different jilaces. 

" Another object of this Society will be to avail itself of every 
0]iportunity of establishing observatories in those parts of the world 
where none are at present in existence. 

" Other beneficial results to be expected from a Society of this 
kind are, the diffusion of a spirit of inquiry concerning tlie use of 
instruments, the practice and extension of meteorological researches, 
and the encouragement of mutual information among its members." 

The number of Members already exceeds one hundred ; and the 
List of Officers for the year is the following : — 

President. — Samuel Charles Whitbread, Esq., F.R.A.S. 

Vice-Presidents. — General Sir Thomas M. Brisbane, Bart., K.C.B., 
F.R.S.; Lord Robert Grosvenor. M.P. ; Luke Howard, Esq., F.R.S.; 
Hastings Russell, Esq., M.P. 

Treasurer.— .^ohn Lee, Esq., LL.D., F.R.S., F.R.A.S. 

Secretary.— i^xne^ Glaisher, Esq., F.R.S., F.R.A.S. 

Council. — Capt. Francis Blackwood, R.N., F.R.A.S. ; Rev. Pro- 
fessor T. Chevallier, B.D., F.R.A.S. ; John Drew, Esq., F.R.A.S. ; 
Vincent Fasel, Esq., F.F..A.S. ; Rev. Samuel King, M.A., F.R.A.S. ; 
George Leach, Esq., F.Z.S. ; Edward Joseph Lowe, Esq., F.R.A.S. ; 
Rev. Charles Lowndes, M.A., F.R.A.S. ; Rev. Josejih Bancroft 
Reade, ALA., F.R.S. ; William R utter, E,?q., F.R.A.S.; Thomas 
Shapter, M.D. ; Professor John Stevelly, LL.D. 

VII. Intelligeiice and Miscellaneous Articles. 


^ '^HE Tuscan Lagoons are, pro])erly speaking, natural depressions 
•^ of the soil ordinarily filled with water from which hot vapours are 
ejected. TJiey are situated within a space of ten or twelve miles, 
lying between 28° 27' and 28° 40' of longitude, and between 43° 10' 
and 43° 15' of latitude. The principal lagoons are those of Monte 
Cerboli, of Castel Nuovo in the valley of Cecina, those of Sasso, of 
Monte Rotondo, of the Lago del Edifizio, of Lustignano and of Ser- 
razzano in the valley of Cornia. The ancients were acquainted 

Litelligejice and Miscellaneous Articles. 73 

with the Tuscan lagoons, and the name of Mount Cerberus accords 
well with the poetical and mythological ideas of the early people of 

Even as late as the 1 8th century the lagoons were regarded only 
as a suj^ernatural wonder which excited astonishment rather than 
courted investigation. Under the Grand Duke Leopold I., the 
chemist Hoefer discovered by analysis, that they contained boracic 
acid. This discovery, followed by further explorations, has bestowed 
upon the lagoons an unrivalled industrial importance, and has brought 
into the countries possessing them an activity contrasting strikingly 
with the miserable state in which they before languished. It is a 
curious fact in tlieir history that before the discovery of this acid, 
the fcetid odour developed by the sulphuretted hydrogen gas, — the 
certain death which met the man who fell into the scalding baths, — 
the disruptions of the ground occasioned by the appearance of new 
Sqffioni, — and above all the superstitious terror with regard to them, 
had made the people consider the lagoons as a scourge from which 
they sought deliverance by public prayers ; but now, if by any cause 
the Fumacchi, the source of common prosperity, should become ex- 
tinguished, they would not fail to seek from heaven a restoration of 
this scourge, which in the skilful hands of AI. Larderel, has become, 
to quote M. Bowriiig, a source perhaps of greater riches than the 
mines of Peru or of Mexico, and certainly more reliable. After the 
discovery of Hoefer, Paul Mascagni, a noted chemist, had the first 
idea of procuring from the lagoons boracic acid like that of China, 
and of thus restoring to Europe the tribute that she had paid to 
Asia. But the attempt was not at first profitable, as the waters con- 
tain in solution at the moment of their escape from the earth, only 
an insignificant quantity of boracic acid. Another chemist having 
observed that a part of the acid was thrown beyond the lagoon, by 
the violence of the vapours, and that it was scattered on the mar- 
gins of the craters, and moreover being confident that the waters 
were capable of dissolving a greater quantity of acid, endeavoured 
to find means of saturating them by constructing upon the declivi- 
ties of the country artificial lakes fed by the streams from the moun- 
tain. The vapours which issue from these lakes keep their waters 
constantly at a boiling temperature. After impregnation for twenty 
or thirty hours by the vai)ours of the highest lake, they draw pfF the 
waters into the second lake to submit them to a new impregnation. 
From thence they are drawn into a third, and so on till they reach 
the receptacle at the lowest point. In their passage across six or 
eight lakes, they are charged with half per cent, of boracic acid. 
They are then led into the reservoir from which they are conducted 
into lead reservoirs for evaporation, to jjroduce concentration ; and • 
to hasten that operation, the happy idea was proposed of substi- 
tuting for the combustibles sometimes used, and which were enor- 
mously expensive, the direct application of the heat of the Soffioni. 
This improvement decided the success of the enterprise. It is sur- 
prising tliat it was introduced at so late a day, since this method 
was not new and had been long practised at the solfatara of Poz- 
zuoli in extracting alum from the earth that contains it. In the 
lagoons, the hot vapours for carrying on the evaporation are taken 

74 Intelligence and Miscellajieous Articles. 

at their origin and carried across by lead jjipes or by subterranean 
conduits below the boilers. Thus the fabrication is extremely t^implc, 
the locality itself furnishing the means of carrying it on. A single 
discharge of the vapours is sufficient to throw into ebullition, almost 
immediately, 20 or 30 caldrons of a capacity of 20 barrels, which 
may be estimated at 84,000 pounds of liquid impregnated with bo- 
racic acid. Before allowing tlie vai)ours to escape, they direct them 
under the ovens in order to free the acid from its hygi-ometric moist- 
ure. Of late the somewhat complex system of boilers and coolers 
has been simplified by substituting rectangular tables of lead of 20 
or 30 metres, divided at small intervals by transverse parallel divi- 
sions, but whose height is never raised above that of the edges. These 
tables have an inclination of two to three degrees. The water of the 
last lagoon is introduced upon the upper side, in small quantities. 
The hot vapours for evaporating arc conducted in such a manner that 
they act upon the lower surface. The liquid after having tilled the 
first compartment is diffused very gradually into the second, then 
into the third, and so successively to the last, where it reaches such 
a state of concentration that it deposits the crystallized acid ; the 
workmen remove it immediately by means of wooden scrapers. This 
mode of gradual concentration is very ingenious, and requires so few 
hands that it may almost be said that the acid is obtained without 
expense. From 1818 to 1845 the quantity of acid manufactured was 
33,349,097 Tuscan pounds. From 1839 to 1845 the mean quantity 
has been two millions and a half of pounds. 

Thus in estimating the product at 7500 pounds per day, the 
quantity of saturated water upon which they operate daily is 
1,500,000 lbs. daily, and annually 547,500,000 lbs. 

This labour brings to Tuscany 12 millions of pounds (10 millions 
of francs), and it is surprising that it should have remained unpro- 
ductive during so many ages, and that it should have been reserved 
for the skill of M. Larderel, now Count of Monte Cerboli, and before 
1818a simple wandering merchant, entirely unacquainted with scien- 
tific researches, to discover the fugitive vapours and render them a 
source of inexhaustible wealth. 

The violence with which the burning vapours escape gives rise to 
muddy explosions, when a lake has been drained by turning its 
waters into another lake. The mud is then thrown out, as solid 
matters are ejected from volcanos, and there forms in the bottom of 
the lake a crowd of those little cones of eruption whose activity and 
play recall exactly under another form the hornitos of Malpays. 
Their temperature varies from 120° to 145° centigrade, and the 
clouds which they form above the lagoons constitute true natural 
barometers, whose greater or less density rarely disappoints the pre- 
dictions that thej- announce. 

While in an industrial point of view, the lagoons occupy the first 
rank among the natural products of Tuscany, they place new re- 
sources at the disposition of science, permitting the investigation of 
various geological phcenomena, even under the direction of the will 
of the experimenter. The metamorphic gypsum which we have seen 
produced at Pereta under the influence of sulphuretted hydrogen 
vapours, is formed at the lagoons, which, like those of Monte Cerboli 

InieUigence and Miscellatieons Articles. 75 

and of Castel Nuovo, are made to cross argillaceous limestone beds, 
and with such abundance that their formation may be fully tested. 
Action also takes place at the same time u])on the walls of fractures 
and the fissures of the soil which open a passage to the subterranean 
vapours. Thence it extends gradually into the interior of the masses, 
and it ends by gypsifyiug whole circles whose I'adius is generally 
that of the lagoons themselves. Pure limestones are converted into 
a lamellar sulphate of lime, but of a loose texture and free of cel- 
lules. This structure is probably due to the expansion they undergo 
from the addition of new materials, and perhaps also by the passage 
of the gas at the moment of the crystallization of the salt. The cal- 
careous formations below the argillaceous, preserve after their trans- 
formation their primitive position, and they present an alternation of 
gypseous beds, and of argillaceous beds which the acid has freed 
from the soluble bases. When this influence is exerted in the direc- 
tion of the thickness of the strata, it is very common to see towards 
the limits where the metamorphic influence ceases, a mass of rock 
strikingly calcareous at one of its extremities, terminating at the 
other extremity in a gypsum which the inhabitants use for buildings. 
The resemblance to the gypsum beds, occurring in the midst of the 
secondary formations, is exhibited even in the reddish tint with 
which oxidation marks the associate clays of the ali)erese. But a 
peculiarity which has given me the solution of a problem which had 
embarrassed me thus far, deserves mention ; for we have reproduced 
here certain phaenomena of which the enormous deposits of the Pro- 
ven9al Alps present many examples. I had noticed at Roquevaire 
and at Digne, in-egular argillaceous incrustations in which are found 
entangled without order, angular fragments of sulphate of lime of 
various sizes. In admitting the transformation of the Jurassic lime- 
stone of these countries posterior to its consolidation under the in- 
fluence of the acid vapours, it was difficult to explain the mode of 
formation of these breccias and the manner in which these fragments 
were introduced. In all these cases they seemed to indicate an 
overflow of waters, but the theory opposes the intervention of waters 
for the accomplishment of the facts relative to the conversion of the 
limestone, or it leaves in doubt the part which they must have acted. 
But, observe what is appareht at the lagoons of Alonte Cerboli and 
of Castel Nuovo. At the same time that the limestone is changed 
into gypsum, by the contact of sulphurous agents, the fragments of 
alberese which waters had brought down from heights above to the 
midst of the miry and boiling lakes, are thus changed into sulphate 
of lime, and constitute, with the clays in which they sink, brecciated 
argillo-gypseous beds without stratification. That this fact should 
be equally apparent in the ancient beds under analogous circum- 
stances, is at least what might be inferred from the examination 
of that which passes in the lagoons. We should also observe 
the analogous positions of the boracite of Luneburg, which is found 
in crystals disseminated in gypsum intercalated in the midst of a 
cretaceous bed, and the boracic acid and borates of the Tuscan 

These diff'erent facts well confirmed, establish in my view an inti- 

76 hitelligence and Miscellaneous Articles. 

mate resemblance between the gypsum of the lagoons and the ab- 
normal gyjisum beds of secondary regions. 

If the silicitication of the Macigno which we have noticed in the 
neighbourhood of the solfatara of Pereta should appear an exag- 
gerated ajiijlication of the theory brought forward, the verification 
of it may be traced in the lagoons of Sasso, where the solution of 
the si lex of the freestone and its redeposition arc manifest in all 
])laces where circumstances allow of this double transformation. The 
Fumacci of Sasso rise, to the south of the establishments, from be- 
neath a vast mantle of fine-grained freestone, over which passes the 
mountain road connecting the vallej^ of the Cornia w^ith the Province 
of Sienna. At intervals the road is interrupted by isolated boiling 
pools or shallow cavities, which exert a metamorphic action upon 
the region which they traverse. The first evidence of alteration is 
apparent in the colour of the rock, which from blacki^h-gray becomes 
white. It is cracked in all directions. The vapours follow quickly 
these lines of separation, attack the silica of the macigno, dissolving 
it out, and immediately depositing it under a gelatinous form. The 
gelatinous mass becomes opake in the air and assumes the resin-like 
appearance i)eculiar to hydrated silica. In connexion with this we 
observe imbedded in a siliceous cement, nuclei of a white micaceous 
sandstone unaltered at the centre, causing a breccia appearance. This 
kind of breccia is finally, by the complete solution of the nuclei, 
converted into a grayish rock entirely siliceous, which resounds under 
the hammer like clink- stone, and resembles exactly by its aspect and 
its roughness of touch, porcelain biscuit, Sometimes the solution is 
more rapid, and then the rock is formed of an agglutination of little 
grains analogous to those of an ancient quartz rock and possessing its 
tenacity and hardness. Examined with a glass, each grain is composed 
of an independent particle or driblet of hydrated silica, and they 
seem to have collected as viscous tears, such as would have adhered 
together in hardening. Breislak observed at the solfatara of Poz- 
zuoli fragments of decomposed lava bound together by a siliceous 
substance almost vitreous ; but in the lagoon of Sasso the solution 
and permanent regeneration of silica, efl'ected at the expense of the 
macigno, are carried on upon a vast scale and over a space of great 
extent. — Bull. Soc. Geol. de France, Dec, 1848, 147 ; and Silliman's 
American Journal of Science for May, 1850. 


It is readily demonstrated that in any entirely homogeneous me- 
dium, the component parts of which act on each other by forces va- 
rying as any function of the distance, Mariotte's law must i)revail. 
Both elastic tension and cohesive force will necessarily vary as the 
density, in a medium assumed as homogeneous, quite irrespective of 
the law of force, the variation being expressed in terms of distance 
betw'een the component parts of the medium. Whether the force 
be attractive or repulsive, varying inversely with the first or hun- 
dredth power of the distance, the result is the same j that entire 
homogeneousness nukes Mariotte's law riecessary. 

Intelligence and Miscellaneous Articles. 77 

To prove this : assume a perfcctlj' homogeneous medium whose 
parts exert forces varying as any function of the distance. Assume 
in this an origin of coordinates, three coordinate axes, X, Y and Z, 
and three constant elementary distances, dx, dy, dz. Conceive each 
axis graduated by laying otf its clement successively from the origin 
outward. Through each })oint of graduation on either axis pass a 
plane parallel to the other axes : do this for each axis. The sjjace 
arouncl the origin is thus divided into elementary parallelojiipeds, 
each of which contains a like portion of the homogeneous medium. 

The force of elastic tension or of cohesion is measured by the re- 
sultant action on a unit of surface of the plane X, Y, by all the 
forces acting in the positive direction of the axis Z, between the 
parts on opposite sides of the plain X, Y. This resultant is balanced 
by an equal one acting in the negative direction of the axis Z. To 
make up this resultant, a certain number of the elementary portions 
of the medium conspire. It may therefore be equated with a series, 
each term of which expresses the ])ositive component along the axis 
Z, of the force exerted between two elementary portions of the me- 
dium on opi)osite sides of the plane X, Y. 

If now the density of the medium be varied, each tei"m of this 
series will vary in the same ratio, since the quantity of matter in 
each elementary volume varies as the density. The density thus 
governs each term of the series, by fixing the quantity of matter in 
each elementary volume. If we call the ratio of the varying density 
to a standard density N, each term of the series contains N as a 
simple factor ; or the whole series varies as N. Hence the resultant 
or entire elastic tension or cohesion varies as N, or as the density. 
This result is entirely indejiendent of any particular law of relation 
between the forces and distances ; and will always be true so Ion"* 
as the elementary volumes can be assumed as homogeneous. As 
dx, dy, dz can always be taken indefinitely less than the radius 
of sensible activity of any assumed force, the demonstration can 
only fail by the parts failing to be homogeneous. 

It will be seen by the above, that any inference of the law of re- 
pulsive force between ultimate atoms or molecules, cannot be cor- 
rectly drawn from Mariotte's law, for this leaves the primary forces 
involved wholly indeterminate. We are by no means authorized to 
conclude, that ia elastic fluids, where the 2)ressure varies as the 
density, the molecules repel each other directly as the distance. 

The demonstration now given has a singular bearing on the 
atomic theory of material constitution. ^Ve know experimentally 
that Mariotte's law does not prevail uniformly in elastic media, while 
in liquids and solids it has no show of application. Hence we are 
bound to infer non-hoinogencousness. Now how can homogeneous- 
ness be interrupted, except through something like an atomic con- 
stitution of media } A laminated, filamental, or molecular structure 
alone can produce heterogeneousness. The two first would confer 
special properties in certain directions, which are not found in fact. 
Hence a molecular constitution of matter seems entailed as an in- 
ference, from the bare fact that Mariotte's law is not universal. 
According to the view now presented, the elasticity of gases varies 
as the density, because the quantity of matter within the sphere of 

78 Intelligence and Miscellaneous Articles. 

sensible activity varies in that ratio. As they approach the point of 
liquefaction, other considerations derived from the special atomic 
constitutions of the media must be introduced. The entire absence 
of a limit to the division of parts would produce that homogeneous- 
ness from which Mariotte's law becomes an inevitable inference. 
Such an inference, as applied to media in general, being contrary to 
the fact, a limit to actual division of parts must be admitted. Any 
other ifieory than one of ultimate molecules, separated by spaces, seems 
to impose inferences conflicting irith facts, throwing vs back irresisti- 
bly into the theory of true moleiiihtr structure. — Silliman's American 
Journal, May, 1850. 

Boston, April, 1850. 


The Revue Scientifique for December last contains an interesting 
article by M. Baumgartner on the subject of the effects of atmo- 
spheric electricity upon the wires of the magnetic telegraph. The 
following are the most interesting of his results : — 

1. The needle rarely coincides with the point which is determined 
by its astatic state and the tension of its suspension thread ; almost 
always it deviates more or less from this point, which proves that 
it is influenced by an electric current. 

2. The variations are of two kinds ; there are some which reach 
50°, others extend over \° or 8'. The first are less frequent; they 
differ so often in direction and intensity that it is impossible to de- 
duce a law for them. On the contrary, the small deviations appear 
connected by a very simple law\ 

The observations made at Vienna and at Gratz appear to show 
that, during the day, the electric currents move from Vienna and 
from Gratz to Semraering, which is more elevated. This direction 
is inverse during the night. It appears that this change of direction 
takes place after the rising and setting of the sun. 

3. The regular current is less disturbed by the irregular currents 
when the air is dry and the sky is serene, than when the weather is rainy. 

4. In general, the curi'ent is more intense with short than with 
very long conductors ; often, even, the current of the longer chain 
is opposed to the current of the shorter chain. 

Where there is a difference of intensity, this difference is far 
greater than that which could originate from the resistance of the 
longer conductor. 

When the sky is cloudy and the weather stormy, there are fre- 
quently observed in the electric conductor currents which are suffi- 
ciently intense to affect the telegraphic indicators, which are, how- 
ever, far from having extreme sensitiveness. 

When they were placing the conducting wires of the Northern 
Telegraph line from Vienna, the workmen frequently complained of 
a kind of spasms which they felt in handling the wires. These 
spasms ceased as soon as they took the precaution not to touch the 
wires with naked hands. These spasms were most frequent and in- 
tense in Styria, the highest region of the line. Thus, near Kranich- 
feld, a workman received a shock sufficiently violent to overturn him 
and paralyse his right arm. 

Meteorological Observations. 79 

The action of the atmospheric electricity on the telegraphs is 
stronger on the aj)proach of a storm ; and not unfrequently the wires 
themselves, and tlie poles which support them, are destroyed by 
electric discharges. 

M. Baumgartner cites several examples in support of what has 
just been said. On the 17th of August 1849, a storm which had 
burst forth at Ollmutz extended to Frielitz, that is to say, to a di- 
stance of ten miles. A workman emjjloyed at this latter station, in 
putting up the wires experienced a shock which overturned him, 
and he experienced a real burn of the fingers which touched the 
wire. At this time the sky w'as perfectly serene at Frielitz. — From 
the Journal of the^FrankUn Institute for April 1850. 


Chiswick. — May 1 . Cloudy and cold. 2. Fine : clear : frosty. 3. Clear : very 
dry air: overcast: sharp frost at night. 4. Fine: showery. 5. Cloudy: some 
angular hail at 6 p.m. 6. Constant rain. 7, 8. Drizzly. 9. Heavy clouds : 
fine: clear. 10. Clear: cloudy. 11. Fine. 1'2. Slight shower : fine. 13. Fine: 
very dry air : rain at night. 14. Cloudy and fine. 15. Fine : cloudy : clear and 
frosty. 16. Fine. 17. Overcast. 18. Foggy: rain: cloudy. 19. Very fine: 
cloudy. 20. Uniformly overcast : fine: clear. 21. Fine: cloudless: overcast: 
rain. 22. Rain : clear at night. 23. Cloudy : clear. 24. Slight fog: dry haze. 
25. Cloudy : fine : showery. 26. Showery : overcast. 27. Cloudy : overcast. 
28. Fine : showery : clear. 29. Cloudy and fine. 30. Foggy : dry haze : clear. 
31.- Fine : slightly clouded. 

iNlean temperature of the month 51°*14 

INIean temperature of May 1849 55 -19 

Mean temperature of May for the last twenty-tliree years . 54 '22 
Average amount of rain in May 1*84 inch. 

Boston, — May 1. Cloudy. 2,3. Fine. 4. Cloudy: rain early a.m. 5. Cloudy: 
rain P.M. 6. Cloudy: rain a.m. 7,8. Rain: rain a.ji. and p.m. 9. Rain: 
rain A.M. 10,11. Cloudy. 12,13. Fine. 14. Rain a.m. and p.m. 15. Rain: 
rain A.M. 16. Fine. 17—19. Cloudy. 20. Rain: rain a.m. 21. Cloudy. 
22. Cloudy : rain a.m. 23. Fine. 24. Fine : rain p.m. 25, 26. Cloudy : rain a.m. 
27. Cloudy : rain a.m. and p.m. 28. Fine. 29. Cloudy : rain p.m. 30. Fine. 
31. Cloudy. 

Api'legarth Manse, Dumfries-shire. — May 1. Slight frost : very cold east wind. 
2. Slight frost : wind changed to west p.m. 3. Frost still : slight shower p.m. 
4. Cold and ungenial : one sharp shower. 5. Frost : fall of snow : hills white. 
6. Frost: clear and cold. 7. Frost hard : is this May? 8. Cloudy a.m. : hail : 
rain p.ji. 9. Frost hard again : most unseasonable. 10. Heavy rain : cleared p.m. 
11. Rain in the night : slight shower a.m. 12. Occasional sharp showers. 13. 
Cold : fair and clear. 14. Fair and clear : keen and cold p.m. 15. Frost again : 
hail : keen and cold. 16. No frost : cloudy: mild. 17. Fine: cloudy: mild. 
18. Fine : air feels moist. 19. Shower in the night : cold east p.m. 20. Parch- 
ing cold east wind. 21, Warm and sultry: change great. 22. Very warm: 
thunder and heavy rain. 23. Very warm : thunder : a few drops, 24. Very 
warm : fair and fine. 25. Soft rain all day : genial and growing, 26. Soft rain 
all day : !)lessed change of weather. 27. Rain : fair p.m. 28, 29. Fair through- 
out: fine. 30. Fine : thunder: shower. 31. Fine : thunder : a few drops. 

INIean temperature of the month , 49°*1 

Mean temperature of May 1849 50 '5 

Mean temperature of INIay for the last twenty-eight years ... 51 "1 
Average rain in May for twenty years 1-69 inch. 

Saitilu'ic/c Manse, Or/i)iei/. — May 1. Clear: fine. 2, Fine : clear, 3. Showers : 
sleet-showers. 4, Hail : snow-showers. 5, Snow : snow-showers. 6. Clear : 
drops, 7. Clear: showers, 8, Damp: clear. 9. Frost: clear: cloudy. 10. 
Cloudy : drops. 11, Showers : hail-showers. 12. Showers : sleet-showers, 13, 
Bright : rain : clear. 14. Clear : rain : clear. 15. Bright : cloudy. 16, Damp, 
17. Fine, 18. Cloudy: fog. 19. Hazy, 20. Bright. 21, Bright: showers: 
fog. 22, Fine : fog, 23. Cloudy. 24, Hazy : fog. 25. Hazy : rain. 26. Hazy. 
27. Cloudy : fine. 28—31. Bright ; fine. 





o m — 

fe- > 

a s: 

C si- i ^ ?i 5? '^ S >• 5: i fe fc* = ? &' ^ ^ a; o 

: fe 

Qj CA tfl U3 CA O ^ 

•UfJ t 

I I ^ ""* '1' 
^ ^ s" c c 
J: S !S ^ 

I fe 5:* I S E'" 


OJ o ^ > 
C C in S 

.« a 

o ? 





.-<LOO^'^'lOlnlOtn<^^(Ncooc^Oln^o^~t^r^oooooooloc»o^(NO'. cici'* 

p-^ r^^i -.W -•'« --CJ -ti r-kn »«1« -'CJ -^IN r-lei ^t« «lti m!« -tie* -^lo ^tei r-Ioi 

t^— e^>0<^lO0000O^0^r^^^^O0lOOlOt^l0(^l^O<^tlCOt^O^O^OO— "00 

•ui-B ?8 


o S 



O00r-O«O00t-^r!<-^inOM3M^-^— OlOr^OfMCM'^COOOM/JOOCXDOs 

•lUB ^8 



o — 

in 00 CO 

— C< CO 

— t^ lO 

O 00 C^(M 

to 'S'ur' -^ 

UO tT CO t~ 

Ch O) >0 fN 

lO lO '-fOO 

o OS a\ o 

O <N 

6 6 


— OS r^ 

— . r^ i^ CO t^ — CI o-i 

00 OM^ CO CTi CO O O 

JO sXbq 


1' H E 





AUGUST 1850. 

VIII. On the Aerometric Balance, an instrument for measuring 
the Densitij of the Air in ivhich it is situated. Bij Professor 
Potter, A.M., late Felloxo of (Queen's College, Cajnbridge^. 

THAT the density of the air is an important element in 
every discussion of atmospheric phasnomena, will at once 
be admitted ; hut it will be often maintained also, that we have 
the means of determining it from observations of the wet and 
dry bulb tiiermometers and the barometer. A little reflection 
will, however, soon convince us that this is not absolutely true, 
since it supposes a regular constitution of the atmosphere for 
all localities and all states of the weather, which certainly does 
not exist. Thus, in a room where many persons have been 
for some time assembled, the carbonic acid gas coming from 
their lungs in respiration will increase the densiij' of the air 
in the room; but this will not affect the thermometer, or in a 
sensible degree the barometer. 

There are many natural localities on the earth where ex- 
halations affect the density of the air, but of which the pre- 
sence escapes detection by the before-named instruments ; and 
at all places we shall find, dn consideration, that the density 
of the air depends on circumstances not necessarily shown to 
exist by them. If, for instance, the barometric pressure and 
the temperature were given, we might still have ixnnpper cur- 
rent of wind which had a particular hygrometric state and a 
particular proportion of its constituent gases, whilst the lower 
current of wind was of another composition. The varying den- 
sity of the lower current would clearly not be indicated by 
the usual meteorological instruments. 

These cases would be comprehended in the discussion of 
the formula /? = /p(l +«§°) for the relation of the pressure, 

* Communicated by the Author. 
Phil, Mag. S. 3. Vol. 37. No. 248. August 1850. G 

82 Professor Potter on the A'cromelric Balance^ 

density, and temperature of a gas, by the consideration that 
wliLMi it is applied to a mixture of gases, such as the atmo- 
sphere, the vahie of /.• is dillerent lor every variation in the 
proportions of the elements. 

'i'he method of weighing a known volume of the air, which 
has been admitted into a flask partially exhausted by the air- 
pump and then weighed, is one of considerable labour, and 
requiring the greatest degree of care in order to obtain correct 
results. An instrument which would give the actual density 
by a simple reading of!" is evidently so great a desideratum, 
that the instrument about to be described has probably in 
some shape or other suggested itself to others, though no in- 
strument of the kind is used at present amongst the recog- 
nized meteorological instruments that I am aware of. 

The new instrument is a modification of an old air-pump 
experiment, which is used to show that the greater buoyancy 
of more bulky over denser bodies of equal weights in the air 
is a considerable and a measurable quantity. A metallic body 
hanging at one end of a balance appears in the air to be 
heavier than a closed hollow globe of glass hanging from the 
other end ; but when placed under the receiver of an air- 
pump, and the pump is woiked, it is soon seen that as the air 
is withdrawn the apparent excess of weight becomes less and 
less, and eventually the hollow globe preponderates. In an 
instrument for determining the variable buoyancy of bodies 
in the lower stratum of the atmosphere, the points to be sought 
for in the construction are, a sufficient sensibility and a means 
of determining the results with readiness. A large closed 
globe of glass might be weighed at different times in a fine 
chemical balance; but the process would be tedious, and from 
perpetual changes in temperature, susceptible of less nicety 
than that of a delicate bent lever balance, such as I have 

There arise difficulties in the construction when extreme 
sensibility is desired, which a knowledge of the mechanical 
properties of balances, and a confidence in their theory, alone 
can be expected to surmount. For instance, in tlie trials 
which have been made with the instrument constructed by 
Messrs. Watkins and Hill from my drawings, we have found 
a position of stable equilibrium and another of unstable ecjui- 
librium within an angle of 40 degrees. The theory showing 
that no such positions of equilibrium can exist in a perfect 
balance, the result indicated that the knife-edges of the balance, 
or the agate planes in contact with them, though made with 
all the care considered requisite in fine chemical balances, 
were yet not sufficiently true for such a degree of sensibility; 

an instrument for measuring the Density of the Air. 83 

and that even with a less degree of sensibility it was requisite 
to have the knife-edges sharper, straighter, or more nearly 
parallel, and the agates more accurately flat; — these points 
were accomplished by improved methods of preparing the 
parts above named. 

The annexed figure is a side view of the essential parts of 
the instrument. A is a hollow globe of glass of about 47} 

inches diameter, hermetically sealed, having an eye in the 
upper part where the tube from which it was blown has been 
sealed : by this eye it is suspended by hooks from a steel stem 
fixed to the brass frame 13, holding an agate plate. This 
agate plate rests on the knife-edge of the triangular prism of 
steel as in the figure. C is another triangular prism of steel 
fixed like the former to the brass lever of the balance. The 



Professor Potter on the Aerometric Balance, 

knife-edfije at C rests on another agate-plate held by the frame- 
work of the inslrnment. The end D of the lever is formed so 
as to be oraduateii as a vernier ; and a graduated arc having its 
centre at the knife-edge C is fixed firmly in a vertical jilane 
to the brass framework. The readiniis of the iii'tnluateil arc 
by means of the vernier give the position of e(|uilibriLim of the 
lever. At a 6 is a fine steel screw passing through the arm 
of the lever and carrying a brass head at b; this screw, turned 
by a key, regulates the sensibility of the balance by raising or 
lowering the centre of gravity of the lever. The spirit-levels 
for adjustment to the horizontal position, as well as other de- 
tails, are not drawn in the figure. 

The whole balance is fixed firmly in a glass case or 
lanthorn, which also contains its accompanying thermometer. 

The instrument evidently acts by the changing weight of 
the air displaceil by the globe with its appendages, and the 
lever. If these volumes were exactly known, and the place 
of the centre of gravity of that displaced by the lever for given 
temjDeratures, then the density' of the air could be calculated 
from the position of equilibrium ; but since these cannot be 
easily determined with accuracy, the method of employing the 
instrument must be that of finding the value of its divisions in 
terms of the density of the air, by cxperimciilal methods, for 
changes of temperature and pressure; such as by examining 
the instrinnent under the receiver of an air-pump furnished 
with a barometer gauge, and by noting the eflfect of change of 
temperature in the lanthorn when the atmospheric pressure is 

In investigating the theoretical sensibility of the bent lever 
balance, I shall first suppose, in the ordinary way, that the 
weights are absolute weights, and afterwards take the modifi- 
cation introduced by supposing the balance used, as actually, 
in a medium of varying density. 

Let c be the fulcrum, b the point from which the globe and 

an instrument J'or measuring the Densitij of the Air. 85 

its appendages hang, their weight being m'; let g be the 
centre of gravity of the beam at which its weight xo acts; let 
cb = r', cg = r. Drawing the straight lines bed and cg^ let the 
angle dcg = a; also drawing the horizontal line McN, let the 
angle Med {= angle Ncb) = 6. 
Then in equilibrium, 

texcM = to' xrN, 

TO X r cos {a. + S)= to' X r' cos 6, 

/, 'w'.r' \ 

.-. tan 9= cot a I 1 I ; 

\ w.?-.cosa/ 



1 +a'. 

where .v will be a small fraction, positive or negative; we have 






Here 6 = when 

2 sin «' 

.t-=— 2SU12-; 

also for a given value + of .r, 9 changes very rapidly for cor- 
responding changes in the value of « when this latter is very 
small : or the sensibility increases very quickly when the 
points i, c, and g are brought very nearly into one straight 

Again, let to and to' be the apparent weights in air, and let 
TO, and Wg be the absolute weights; so that to = to,(1— 7w), 
to' = to.,(] —n)^ where by the laws of hydrostatics m'w^ is the 
weight of the air displaced by the beam supposed of homo- 
geneous materials from which it differs very slightly, and ?iTO'2 
that displaced by the globe and appendages; 

specific gravity of air a 

or m— — L,^^ "^ — \ = J- say; 

specihcgravity orthe beam b 

specific iiravitv of air a 

11 — __ ' » J. = _ say. 

specific gravity of globe and appendages c 

86 Professor Potter on the Aerometric Balance^ 

Here vi and n are small quantities, but m much smaller 
than ?/, so that 

isy . r 
M' . r 

~ Wi.r(l —m) 

tu., . r' 

= -f — (\ — n — ni) nearly 

and the value of .r will be continually changing as the value 
of rt, the specific gravity of the air, changes, whilst the frac- 

tion ■ ^' remains constant, and the changes in h and c are 

almost imperceptible in comparison with those of a : or 6, with 
the position of equilibrium, will continually change with the 
density of tlie atmosphere. 

The degree of sensibility may be any that is wished, pro- 
vided weights are added to, and taken away from the end B, 
which weights might be very conveniently laid upon the plate 
containing the agate plane. In some trials I had the index 
moving through 40^ with i grain difference in the weight 
hanging from B ; and this is equivalent to a change of about 
one inch in the height of the barometer, or between 16° and 
17° of Fahrenheit's thermometer. 

When changes in the density of the air are required to be 
found which are not dependent solely on temperature and 
pressure, but also on occasional admixtures in the air sur- 
rounding the balance, we have to compare its indications with 
those of the other named instruments, and it is needless to 
have a greater sensibility than theirs. Now the best baro- 
meters read only to one-thousandth of an inch in the height 
of the mercurial column, antl the best thermometers can 
seldom be depended upon to one-hundredth of a tiegree 
Fahrenheit; so that if i a grain added at B cause the index 
to move through iO'^ otarc, and we read the vernier to \ mi- 
nutes, we have an accuracy greater than either of the other 
named instruments, and one which is sufficient for our expe- 
riments. In this case the scale of 60^ will suffice for the 
changes which occur in this climate, without need of weights 
in addition. 

an instrument for measuri?tg the Density of the Air. 87 

The following table contains tiie last series of observations 
which I have made previous to the instrument being finished, 
with some additions. The thermometer inclosed in the 
lanthorn was a good one, but not the one intended to be used, 
which was not ready ; it was read with a reading microscope, 
as was also the aerometric balance. The instrument was 
placed in an upper room facing the west, in which no fire was 
lighted. The barometer was a good aneroid one, with an 
attached thermometer. I have not thought it necessary to 
give the readings of these, but only the height of the baro- 
metric column reduced to a temperature of 32°. 

The column of the densities is calculated from the formula 


^ A-(l+«f) 

with unity as the density for 32" temperature and 30 inches 

barometric pressure, takinfj «= for comparison with the 

t ' » 4-90 * 

aerometric balance. Although the changes take the same di- 
rection, that is, greater buoyancy is indicated when there was 
greater calculated density, yet the changes are not propor- 
tional; and on comparing different parts of the series, we see 
remarkable differences. Observations of the iscet hulh ther- 
mometer might have enabled us to explain some of these, by 
the hygrometric changes going on ; but if any remained, they 
would indicate changes in the composition of the air of the 

When Messrs. Watkins and Hill have fjot the construction 
of the aerometric balance perfected, I should feel great interest 
in the results obtained in different parts of the country, but 
must leave the observations to others with better opportunities 
and more time, and rest satisfied with having completed the 
less important task of designing and superintending the con- 
structions of the means of observation. 

The observations of the table have a point of interest in 
having been taken through one period of storm, and another 
of dark but high foix. 

S8 Dr. Faraday's Experimental Researches in Electricitij : 




Density of the 

of the 

itTomc- Ucmtirks. 

trie ba- 


Hour of ob- 1 
serv-ation. i 

ter cor- 
rected to , 
12° tei'ip.; 


iicter in 
the liiii- 
thorii. 1 


air t'rom 

• lc,\+ae°): 

April 12. 

h 111 

8 7 a.m. 


5j-5 1 

-94257 ! 

+ 2 3 Rain, foggy. 

3 18 P.M. 

2;)- 72 

60-9 1 

-93870 1 

3 35 


8 5 a.m.' 


55 3 ! 

-!>."> 1S5 

1 3 

11 25 


56 1 ' 


1 31)ark, but high fog. 

11 34 




1 8 Wind, lighter. 

7 40 P.M. 




1 38 Uiill, rainy. 

11 55 




1 18'riie sauie. 


7 55 A.M. 

29 -13 



1 33 Dull, cloudy. 

3 10 P.M. 




4 13 lias raincil,iu)\v sunshine. 

11 37 




3 29 Clear, starlight. 


8 5 A.M. 




3 4 Wind liigh, with rain. 

2 P.M. 




3 9 Storm and rain. 

3 55 


55 5 


3 37! High wiiul, sunshine. 

5 20 




3 56 Very high wind. 

11 10 




3 7 High wind. 


8 10 a.m. 




2 16 Bright, strong wind. 

1 35 P.M. 




3 13|Fair, sunshine, soniewind. 

11 10 



■9 1005 

3 2 Starlight. 


8 6 A.M. 




52jBright sunshine. 

3 Op.m. 




3 52jThe same. 

IX. Experimental llescarches in Electricitij. — T'-joenty-tliird 
Series. Bij Michael Fauaday, Esq., D.C.L., 

EidlerianProf. Chem. Roijal Institution'''^'. 

§ 29. On tlie iiolar or other condition of diamagnetic bodies. 

26 to. LTOUR years ago I suggested that all the pliaeno- 
-^ meiia preseiitetl by diamagnetic bodies, when sub- 
jected to the forces in the magnetic field, might be accounted 
lor by assuming that they then possessed a polarity the same 
in kind as, but the reverse in direction of, that acquired by 
iron, nickel and ordinary magnetic bodies under the same 
circumstances (24-29. 2430.). This view was received so 
favourably by Pliicker, Reich and others, and above all by 
W. Weberf, that I hiui great hopes it would be confirmed; 
and thougli certain experiments of my own (2497.) did not 
increase that hope, still my desire and expectation were in 
that direction. 

261-1. Whether bismuth, copper, phosphorus, &c,, when 

* From the Plii'osophical Transactions for 1850, part i. ; having been 
received liy the Ro}iil Society Jannary 1, and read March 7 antl 14, 1850. 

t Poggendorft'b Amialcu, iimn-Avy 7, 1848; or Tayloi's Scientific Me- 
moirs, vol. v. p. 477. 

supposed Polar ity of Diamagnetic Bodies, 89 

in the magnetic field, are polar or not, is however an exceed- 
ingly important question; and very essential and great differ- 
ences, in llie mode of action of these bodies under the one 
view or the other, must be conceived to exist. 1 found that 
in every endeavour to proceed by induction of experiment 
from that which is knov.n in this department of science to the 
unknown, so much uncertainty, hesitation and discomfort 
arose from the unsettled state of my mind on this point, that 
I determined, if possible, to arrive at some experimental proof 
either one way or the other. This was the more needful, 
because of the conclusion in the afiirmative to which Weber 
had come in his very philosophical paper; and so important 
do I think it for the progress of science, that, in those imper- 
fectly developed regions of knowledge, which form its boun- 
daries, our conclusions and deductions sl)ould not go far be- 
yond, or at all events not aside from the results of experiment 
(except as suppositions), that I do not hesitate to lay my pre- 
sent labours, though they arrive at a negative result, before 
the Royal Society. 

264-2. It appeared to me that many of the results which 
had been supposed to indicate a polar condition, were only 
consequences of the law that diamagnetic bodies tend to go 
from stronger to weaker places of action (2418.) ; others again 
appeared to have their origin in induced currents (26. 2338.); 
and further consideration seemed to indicate that the differ- 
ences between these modes of action and that of a real pola- 
rity, whether magnetic or diamagnetic, might serve as a foun- 
dation on which to base a mode of investigation, and also to 
construct an apparatus that might give useful conclusions and 
results in res})ect of this inquiry. For, if the polarity exists it 
must be in the particles and for the time permnnent, and 
therefore distinguishable from the momentary polarity of the 
mass due to intiuced temporary currents; and it must also 
be distinguishable from ordinary magnetic polarity by its 
contrary direction. 

264'3. A straight wooden lever, 2 feet in length, was fixed 
by an axis at one end, and by means of a crank and wheel 
made to vibrate in a horizontal j^lane, so that its free extre- 
mity passed to and fro through about two inches. Cylinders 
or cores of metal or other substances, F>}j inches long and 
three-quarters of an inch diameter, were fixed in succession 
to the &\u\ of a brass rod 2 feet long, which itself was attached 
at the other end to the moving extremity of the lever, so that 
the cylinders could be moved to and fro in the direction of 
their length through the space of 2 inches. A large cylinder 
electro-magnet was also prepared (2191.), the iron core of 

90 Di*. I-'araday's Experimental Researches in Electricity : 

wliich was 21 inches long and 1*7 inch in diameter; but one 
end of this core was made smaller for the length of 1 inch, 
biiing in that part only 1 inch in diameter. 

2Gi-t. On to this rediiceil part was fixed a hollow helix 
consisting of 51G feet of fine covered copper wire: it was 
3 inches loiig, 2 inches external diameter, and 1 inch internal 
diameter: when in its place, 1 inch olthe central sjxicc was 
occu})ied by the reduced end of the electro-magnet core 
which carried it ; and the magnet and helix were both placed 
concentric with the metal cylinder above-mentioned, and at 
such a distance that the latter, in its motion, would move 
within the helix in the direction of its axis, approaching to 
and receding from the electro-magnet in rapid or slow suc- 
cession. The least and greatest distances of the moving cy- 
linder from the magnet during the journey were one-eighth of 
an inch and 2*2 inches. The object of course was to observe 
any influence upon the experimental helix of fine wire which 
the metal cylinders might exert, either whilst moving to or 
from the magnet, or at different distances from it'''. 

2615. The extremities of the experimental helix wire were 
connected with a very delicate galvanometer, placed 18 or 20 
feet from the machine, so as to he unaffected directly by the 
electro-magnet ; but a commutator was interposed between 
them. This commutator was moved by the wooden lever 
(2643.), and as the electric currents which would arrive at it 
from the experimental helix, in a complete cycle of motion or 
to and iro action of the metal cylinder (2643.), would consist 
of two contrary portions, so the office of this commutator was, 
sometimes to take up these portions in succession and send 
them on in one consistent current to the galvanometer, and at 
other times to oppose them and to neutralize their result; and 
therefore it was made adjustible, so as to change at any period 
of the time or part of the n otion. 

2646. With such an arrangement as this, it is known that, 
however powerful the magnet, and however delicate the other 
parts of the apparatus, no efiect will be produced at the gal- 
vanometer as long as the magnet does not change in force, or 
in its action upon neighbouring bodies, or in its distance from, 
or relation to, the experimental helix; but the introduction 
of a piece of iron into the helix, or anything else that can in- 
fluence or be influenced by the magnet, can, or ought to, show 
a corresponding influence upon the helix and galvanometer. 

* It is very probable that if the metals were made into cylinders shorter, 
but of hirger diameter than those described above, and used with a corre- 
sponding wider hehx, better results than those I have obtained would be 

supposed Polarity of Diamagnetic Bodies. 91 

My apparatus I should imagine, indeed, to be almost the same 
in principle and practice as that of M. Weber (26iO.'>, cxce})t 
that it gives me contrary results. 

264-7. But to obtain correct conclusions, it is most essen- 
tial that extreme precaution should be taken in relation 
to many points which at tirst may seem unimportant. All 
parts of" the apparatus should have perfect steadiness, and be 
fixed almost with the care due to an astronomical instrument; 
for any motion of any portion of it is, from the construction, 
sure to synchronize with the motion of the commutator; and 
portions of effect, inconceivably small, are then gathered up 
and made manifest as a whole at the galvanometer ; and thus, 
without care, errors might be taken i'or real and correct re- 
sults. Therefore, in my arrangements, the machine (2643, 
&c.), the magnet and helix, and the galvanometer stood upon 
separate tables, and these again upon a stone floor laid upon 
the earth ; and the table carrying the machine was carefully 
strutted to neighbouring stone-work. 

264'8. Again, the apparatus should itself be perfectly firm 
and without shake in its motion, and yet easy and free. No 
iron should be employed in any of the moving parts. I have 
springs to receive antl convert a portion of the momentum of 
the whole at the end of the to and fro journey ; but it is essen- 
tial that these should be of hammered brass or copper. 

2649. It is absolutely necessary that the cylinder or core 
in its motion should not in the least degree disturb or shake 
the exj)erimental helix and the magnet. Such a shake may 
easily take place and yet (without much experience) not be 
perceived. It is important to have the cores of such bodies 
as bismuth, phosphorus, copper, &c., as large as may be, but 
I have not found it safe to have less than one-eighth of an 
inch of space between them and the interior of the experi- 
mental helix. In order to float, as it were, the coi'e in the 
air, it is convenient to suspend it in the bight or turn of a fine 
copper wire passing once round it, the ends of vvhicli rise uj), 
and are made fast to two fixed points at equal heights but 
wide apart, so that the wire has a V form. This suspension 
keeps the core jiarallel to itself in every part of its motion. 

2650. The magnet, when excited, is urged by an electric 
current from five pairs of Grove's plates, and is then very 
powerful. When the battery is not connected with it, it still 
remains a magnet of feeble power, and when thus employed 
may be referred to as in the residual state. If employed in 
the residual state, its power may for the time be considered 
constant, and the experimental helix may at any moment be 
connected with the galvanometer without any current appear- 

92 Dr. Tarailay's Experimental Researches in Electricili^ : 

ing there. But if the mngnet be employed in the excited 
state, certain important {precautions are necessary; for upon 
connectintj; the magnet with the battery and then connecting- 
the experisnental heUx with the galvanometer, a current will 
appear at the latter, which will, in certain cases, continue lor 
a minute or more, and wiiich has the appearance of being de- 
rived at once from that of the battery. Jt is not so produced, 
however, but is due to the time occupied by the iron core in 
attaining its maximum magnetic condition (2170. 2332.), 
thning the whole of which it continues to act npon the expe- 
rimental helix, producing a current in it. This time varies 
with several circumstances, and in the same electro-magnet 
varies especially with the period during which the magnet has 
been out of use. When first employed, after two or three 
days' rest, it will amount to eighty or ninety seconds, or more. 
On breaking battery contact and immediately renewing it, the 
effect will be repeated, but occupy only twenty or thirty 
seconds. On a third intermission and renewal of the current, 
it will appear for a still shorter period ; and when the magnet 
has been used at short intervals for some time, it seems ca- 
pable of receiving its maximum power almost at once. In 
every experiment it is necessary to wait until the effect is shown 
by the galvanometer to be over ; otherwise the last remains 
olsuch an effect might be mistaken for a result of polarity, or 
some peculiar action of the bismuth or other body under in- 

2651. The galvanometer employed was made by Ruhm- 
korff and was very sensible. Tiie needles were strengthened 
in their action and rendered so nearly equal, that a single vi- 
bration to the right or to the left occupied from sixteen to 
twenty seconds. When experimenting with such bodies as 
bismuth or phosphorus, the place of the needle was observed 
through a lens. The perfect communication in all parts of 
the circuit was continually ascertained by a feeble thermo- 
electric pair, warmed by the fingers. This was done also for 
every position of the commutator, where the film of oxide 
formed on any part by two or three days' rest was quitesuffi- 
cient to intercept a feeble current. 

2652. In order to bring the phsenomena afforded by mag- 
netic and diamagnetic bodies into direct relation, I have not 
so much noted the currents produced in the experimental 
helix, as the effects obtained at the galvanometer. It is to be 
understood, that the standard of deviation, as to direction, has 
always been that produced by an iron wire moving in the 
same direction at the experimental helix, and with the same 
condition of the conmiutator and connecting wires, as the 

supposed Polar ittj of Diamagnelic Bodies. 9 3 

piece of bismuth or other body whose effects were to be ob- 
served and compared. 

2653. A thin gLiss tube, of the <,nvcn size (2643.), 5^ by f 
inches, was filled with a saturated solution of jn'otosulphate of 
iron, and employed as the experimental core : the velocity 
given to the macliine at this and all average times of experi- 
ment was such as to cause five or six approaciies and with- 
drawals of the core in one second; yet the solution produced 
no sensible indication at the galvanometer. A piece of mag- 
netic glass tube (^354'.), and a core of foolscap paper, magnetic 
between the poles of the electro-magnet, were equally inefli- 
cient. A tube filled with ssnall crystals of protosulphate of 
iron caused the neetUe to move about 2°, and cores formed 
out of single large crystals, or symmetric groups of crystals of 
sulphate of iron, produced the same effect. Red oxide of 
iron (colcothar) produced the least possible effect. Iron 
scales and metallic iron (the latter as a thin wire) produced 
large effects. 

2654'. Wlienever the needle moved, it was consistent in its 
direction with the effect of a magnetic body ; but in many 
cases, with known magnetic bodies, the motion was little or 
none. This proves that such an arrangement is by no means 
so good a test of magnetic polarity as the use of a simple or 
an astatic needle. This deficiency of power in that respect 
does not interfere with its ability to search into the nature of 
the phoenomena that appear in the experiments of Weber, 
Reich and others. 

2655. Other metals than iron were now employed and with 
perfect success. If they were magnetic, as nickel and cobalt, 
the deflection was in the same direction as for iron. When 
the metals were diamagnetic, the deflection was in the con- 
trary direction; and for so\iie of the metals, as copper, silver 
and gold, it amounted to 60' or 70°, which was permanently 
sustained as long as the machine continued to work. But the 
deflection was not the tjreatest for the most diamaffnetic sub- 
stances, as bismuth or antimony, or phosjihorus; on the con- 
trary, I liave not been able to assure myself, up to this time, 
that these three bodies can produce any effect. Thus far the 
effect has been proportionate to the conducting poiver of the 
substance for electricity. Gold, silver and copper have pro- 
duced large deflections, lead and tin less. Platina very little. 
Bismuth and antimony none. 

2656. Hence there was every reason to believe that the 
effects were produced by the currents induced in the mass of 

f)t- l)i". Faraday's E.vpcriincutal llesearcJics in Elcctricitij : 

the moviiio- metals, and not by any polarity of tlieir particles. 
I proceeded tlieretore to test this idea by different conilitions 
of the cores and the apparatus. 

2657. In the fust phicc, if produced by iiuUiccd currents, 
the great proportion of these would exist in the part of the 
core near to the dominant magnet, and but little in the more 
tlistant parts; whereas in a substance like iron, the polarity 
which tlie whole assumes makes length a more important ele- 
ment. I therefore shortened the core of copper from 5 ', inches 
('2Gt3.) to 2 inches, and lound the effect not sensibly dimi- 
nished; even when I inch long it was little less than before. 
On the contrary, when a fine iron wire, 5h inches in length, 
was used as core, its effects were strong ; when the length was 
reduced to 2 inches, they were greatly diminished; and again, 
with a length of 1 inch, still further greatly reduced. It is 
not difficult to construct a core of copper, with a fine iron wire 
in its axis, so that when above a certain length it should (pro- 
duce the effects of iron, and beneath that length the effects of 

2658. In the next place, if the effect were produced by in- 
duced currents in the mass (264'2.), division of the mass would 
stop these currents and so alter the effect; whereas if pro- 
duced by a true diamagnetic polarity, division of the mass 
would not affect the polarity seriously, or in its essential na- 
ture (24-30.). Some copper filings were therefore digested 
lor a few days in dilute sulphuric acid to remove any adhering 
iron, then well-washed and dried, and afterwards warmed and 
stirred in the air, until it was seen by the orange colour that 
a very thin film of oxide had formed npon them : they were 
finally introduced into a glass tube (2653.) and employed as 
a core. It produced no effect whatever, but was now as in- 
active as bismuth. 

2659. The copper may however be divided so as either to 
interfere with the assumed currents' or not, at pleasure. Fine 
copper wire was cut up into lengths of 5,^ inches, and as many 
of these associated together as would form a compact cylinder 
three-quarters of an inch in diameter (264'3) ; it produced no 
effect at the galvanometer. Another copper core was pre- 
pared by associating together man}' discs of thin copper plate, 
three-quarters of an inch in diameter, and this affected the 
galvanometer, holding its needle 25° or 30° from zero. 

2660. 1 made a solid helix cylinder, three-quarters of an 
inch in diameter and 2 inches long, of covered copper wire, 
one-sixteenth of an inch thick, and employed this as the ex- 
perimental core. When the two ends of its wire were uncon- 
nected, there was no effect upon the experimental helix, and 

supposed Polarity of Diamagnctic Bodies. 95 

consequently none tit the galvanometer ; but when the ends 
were soldered tOii;ether, the needle was well afTected. In the 
lirst condition, the currents, which tended to be formed in the 
mass ot'moviniT metal, could not exist because the metal cir- 
cuit was interrupted ; in the second they could, because the 
circuit was not interrupted; and such division as remained 
did not interfere to prevent the currents. 

2661. The same results were obtained with other metals. 
A core cylinder of gold, made of half-sovereigns, was very 
powerful in its efl'ect on the galvanometer. A cylinder of 
silver, made of sixpenny pieces, was very eflectual ; but a 
cylinder made of precipitated silver, pressed into a glass tube 
as closel}' as possible, gave no indications of action whatever. 
The same results were obtained with disc cylinders of tin and 
lead, the effects being proportionate to the condition ot tin 
antl lead as bad conductors (26,55.). 

2662. Wheniron was divided, the effects were exactly the 
reverse in kind. It was necessary to use a much coarser gal- 
vanometer and apparatus for the purpose ; but that being done, 
the employment of a solid iron core, and of another of the 
same size or weight formed of lengths of fine iron wire (2659.), 
showed that the division had occasioned no inferiority in the 
latter. The excellent experimental researches of Dove* on the 
electricity of induction, will show that this ought to be the case. 

2663. Hence the result of division in the diamagnetic metals 
is altogether of a nature to confirm the conclusion, that the 
effects produced by them are due to induced currents moving 
through their masses, and not to any polarity correspondent 
in its general nature (though opposed in its direction) to that 
of iron. 

2664. In the third place (2656.), another and very im- 
portant distinction in the actions of a diamagnetic metal may 
be experimentally established according as they may be due 
either to a true polarity, or merely to the presence of tempo- 
rary induced currents; and as for the consideration of this 
point diamagnetic and magnetic polarity are the same, the 
point may best be considered, at present, in relation to iron. 

2665. If a core of any kind be advanced towards the domi- 
nant magnet and withdrawn from it by a motion of uniform 
velocity, then a complete journey or fo andyiow action might 
be divided into four parts; the to^ the stop after it; the J'rom, 
and the stop succeeding that. If a core of iron make this 
journey, its end towards the dominant magnet becomes a pole, 
rising in force until at the nearest distance, and falling in force 

* Taylor's Scientific Memoirs, vol. v. p. 129. T do not see a date to tiie 

96 Dr. I'liraday's Experimental Ih'searc/ies in E/ecfiici/jj : 

initil at ilie greatest distance. Both this effect, and its ]uu- 
gressioii inwards and outwards, cause cui'rents to be induced 
in tl)e surioundin«r helix, anil these currents are in one direc- 
tion as the core advances, and in the contrary direction as it 
recedes. In reality, however, the iron tloes not travel with a 
constant velocity ; tor, because of the communication of motion 
from a revolving crank at the machine (2613.), it, in the to 
part of the journey, gradually rises from a state of rest to a 
maximum velocity, which is half-way, and then as gradually 
sinks to rest again near the magnet: — and the Jrom part of 
the journey untlergoes the same variations. Now as the 
maximum effect upon the surrounding experimental helix 
depends upon the velocity conjointly with the intensity of the 
magnetic Ibrce in the end of the core, it is evident that it will 
not occur with the maximum velocity, which is in the middle 
ot the fo OY from motion ; nor at the stop nearest to the domi- 
nant majTuet, where the core enil has jrreatest magnetic force, 
but somewhere between the two. Nevertheless, during the 
"whole of the advance, the core will cause a current in tJje ex- 
perimental helix in one direction, and during tlie whole of the 
recession it will cause a current in the other direction. 

2666. If diamagnetic botlies, under the influence of the 
dominant magnet, assume also a polar state, the difference 
between them and iron being only that the poles of like names 
or forces are changed in place (2429. 24-30.), then the same 
kind of action as that described for iron would occur with 
them ; the only difference being, that the two currents pro- 
duced would be in the reverse direction to those produced by 

2667. If a commutator, therefore, were to be arranged to 
gather up these currents, either in the one case or the other, 
and send them on to the galvanometer in one consistent cur- 
rent, it should change at the moments of the two 5i?o/?5 (2665.), 
and then would perlbrm such duty perfectly. If, on the other 
hand, the commutator should change at the times of maximum 
velocity or maximum intensity, or at two other times equi- 
distant either from the one stop or from the other, then the 
parts of the opposite currents intercepted between the changes 
would exactly neutralize each other, and no final current 
would be sent on to the galvanometer. 

2668. Nov,' the action of the iron is, by experiment, of this 
nature. If an iron wire be simply introduced or taken out of 
the experimental helix with different conditions of the com- 
mutator, the results are exactly those which have been stated. 
If the machine be worked with an iron wire core, the commu- 
tator changing at the stops (2665.), then the current gathered 

supposed Polarity of Diamagnetic Bodies. 97 

lip and sent on to tlic galvanometer is a niaximnni ; if the 
couiniutator change at the moments of nuiximnm velocity, or 
at any other pair of moments e(jui(Hstant from the one stoj) or 
the other, then the current at the commutator is a minimum, 
or 0. 

2669. There are two or three j)recantions which are neces- 
sary to tlie production of a pure result of this kind. In the 
first place, the iron ought to be soft and not previously in a 
magnetic state. In the next, an effect of the following kind 
has to be su^ii'ded aoainst. If the iron core be away from the 
dominant magnet at the beginning of an experiment, then, on 
working the machine, the galvanometer will be seen to move 
in one direction for a few moments, and afterwards, notwith- 
standing the continued action of the machine, will return and 
gradually take up its place at 0\ If the iron core be at its 
shortest distance from the dominant magnet at the beginning 
of the experiment, then the galvanometer needle will move in 
the contrary direction to that which it took before, but will 
again settle at 0°. These effects are due to the circumstance, 
that, when the iron is away from the dominant magnet, it is 
not in so strong a magnetic state, and when at the nearest to 
it is in a stronger state, than the meaii or average state, which 
it acquires during the continuance of an exj)eriment; and that 
in rising or falling to this average state, it produces two cur- 
rents in contrary directions, which are made manifest in the 
experiments described. These existing only for the first 
moments, do, in their efr'ects at the galvanometer, then appear, 
producing a vibration which gradually passes away. 

2670. One other precaution I ought to specify. Unless 
the commutator changes accurately at the given points of the 
journey, a little effect is gathered up at each change, and may 
give a permanent deflection of the needle in one direction or 
the other. The tongues of my commutator, being at right 
angles to the direction of -motion and somewhat flexible, 
dragged a little in the to and ./io/« parts of tlie journey : in 
doing this they approximated, though only in a small degree, 
to that which is the best condition of the commutator for 
gathering up (and not opposing) the currents ; and a deflec- 
tion to the righ.t or left apj^eared (2677.). Upon discovering 
the cause and stiffening the tongues so as to prevent their 
flexure, the effect disappeared, and the iron was perfectly 

2671. Such therefore are the results with an iron core, 
and such would be the effects with a copper or bismuth core 
if they acted by a diamagnetic polarity. Let us now con- 
sider what the consequences would be if a copper or bismuth 

Phil. Ma'y. S. 3. Vol. 37. No. 218. August 1 850. H 

98 Dr. Faraday's Experimental Researches in Electriciti) : 

core were to act by currents, induced for the time, in its 
moving mass, and of the nature ot" those susjiected (2642. )• 
If the copper cylinder moved with uniform velocity (2665.), 
then currents woukl exist in it, parallel to its circumference, 
durinu' the whole time of its motion; and these would be at 
their maximum force just before and just after the to or mner 
stop, for then the copper would be in the most intense parts 
of the magnetic field. The rising current of the copper core 
for the in j^ortion of the journey would produce a current in 
one direction in the expeiimental helix, the stopping of the 
copper and consequent falling of its current would produce 
in the experimental helix a current contrary to the former; 
the first instant of motion outwards in the core would produce 
a maximum current in it contrary to its former current, and 
producing in the experimental helix its inductive result, being 
a current the same as the last there produced ; and then, as 
the core retreated, its current would fall, and in so doing and 
by its final stop, would produce a fourth current in the expe- 
rimental helix, in the same direction as the first. 

2672. The four currents produced in the experimental 
helix alternate by twos, i. e. those produced by the falling of 
the first current in the core and the rising of the second and 
contrary current, are in one direction. They occur at the 
instant before and after the stop at the magnet, /. e. from the 
moment of maximum current (in the core) before, to tlie 
moment of maximum current after, the stop; and if that stop 
is momentary, they exist only for that moment, and should 
during that brief time be gathered up by the commutator. 
Those produced in the experimental helix during the falling 
of the second current in the core and the rising of a third 
current (identical with the first) in the return of the core to 
the magnet, are also the same in direction, and continue from 
the beginning qf the retreat to th^end of the advance (or from 
maximum to maximum) of the core currents, /. e. for almost 
the whole of the core journey ; and these, by its change at 
the maximum moments, the commutator should take up and 
send on to the galvanometer. 

2673. The motion however of the core is not uniform in 
velocity, and so sudden in its change of direction, but, as 
before said (2665.), is at a maxinnim as respects velocity in 
the middle of its approach to and retreat from the dominant 
magnet ; and hence a very important advantage. For its stop 
may be said to commence inmiediately after the occurrence of 
the maximum velocity ; and if the lines of magnetic force were 
equal in position and power there to what they are nearer to 
the magnet, the contrary currents in the experimental helix 

supposed Polarity of Diamagnetic Bodies. 99 

would commence at those points of the journey ; but, as the 
core is enteruig into a more intense part of the field, the cur- 
rent in it still rises though tiie velocity diminishes, and the 
consequence is, that the maximum current in it neither occurs 
at the piace of greatest velocity, nor of greatest force, but at 
a point between the two. This is true both as regards the 
approach and the recession of the core, the two maxima of 
the currents occurring at points equidistant from the place of 
rest near the dominant magnet. 

2674-. It is therefore at these two points that the commu- 
tator should change, if adjusted to produce the greatest effect 
at the galvanometer by the currents excited in the experi- 
mental helix, through the influence of, or in connexion with, 
currents of induction produced in the core; and experiment 
fully justifies this conclusion. If the length of the journey 
from the stop out to the stop in, which is 2 inclies (2643. 
SSii.), be divided into 100 parts, and the dominant magnet 
be supposed to be on the right-hand, then such an expression 
as the following, 50|50, may represent the place where the 
commutator changes, which in this illustration would be mid- 
way in the to and from motion, or at the places of greatest 

2675. Upon trial of various adjustments of the commutator, 
I have found that from 77|23 to 88|12, gave the best result 
with a copper core. On the whole, and after many experi- 
ments, I conclude that w^th the given strength of electro- 
magnet, distance of the experimental core when at the nearest 
from the magnet, length of the whole journey, and average 
velocity of the machine, 86|14 may represent the points where 
the induced currents in the core are at a maximum and where 
the commutator ought to change. 

2676. From what has been said before (2667.)5 it will be 
seen that both in theory and experiment these are the points 
in which the effect of any polarity, magnetic or diamagnetic, 
would be absolutely nothing. Hence the power of submitting 
by this machine metals and other bodies to experiment, and 
of eliniinating the effects of magnetic polarity, of diamagnetic 
polarity, and of inductive action, the one from the others: for 
either by the commutator or by the direction of the polarity, 
they can be separated; and further, they can also be com- 
bined in various ways for the purpose of elucidating their 
joint and separate action. 

2677. For let the arrows in the diagram represent the to and 
from journey, and the intersections of the lines a, h or c, J, &c. 
the periods in the journey when the commutator changes (in 
which case c, d will correspond to 50|50, and e,fx.o 86|14), 
then a, b will represent the condition of the commutator for 


loo Dr, F;ira(l;iy's Experimrntal Rescnrchc^ i)i ElcctricHy : 

the maxiimini ollect ot iron or any other polar body. If the 
line a, b be <i;iaclually revolved until parallel to r, ^/, it will in 
every position indicate 
points of coninuitator 
change, which will give 
the iron eH'ect at the gal- 
vanometer by a deflec- 
tion of the needle always 
in the same direction ; 

it is only when the ends '^ ^' if 

a and b have passed the points c and d, either above or 
below, that the direction of the deflection will change for iron. 
But the line a, b indicates those points for the commutator 
with which no effect will be produced on the galvanometer 
by the induction of c?//7r//i5 in the mass of the core. Iftiie 
hue be inclined in one direction, as /, Jc^ then these currents 
will produce a deflection at the galvanometer on one side ; it it 
be inclined in the other direction, as /, ?/?, then the deflection 
will be on the other side. Tiierefore the effects of these in- 
duced currents may be either combined v<ith, or opposed to, 
the effects of a polarity, whether it be magnetic or diamagnetic. 

2678. Ail the metals before mentioned {2Q55.), namely, 
gold, silvei-, copper, tin, lead, platina, antimony and bismuth, 
were submitted to the power of the electro-magnet under the 
best adjustment (2675.) of the commutator. The effects were 
stronger than before, being now at a maximum, but in the 
same order; as regarded antimony and bismuth, they were 
very small, amounting to not more than lialf a degree, and 
may very probably have been due to a remainder of irregular 
action in some part of the apparatus. All the experiments 
with the divided cores (2658, &c.) were repeated with the 
same results as before. Phosphorus, sulphur and gutta percha 
did not, either in this or in the former state of the commutator, 
give any indication of effect at the galvanometer. 

2679. As an illustration of the manner in which this posi- 
tion of the commutator caused a separation of the effects of 
copper and iron, I had prepared a copper cylinder core 2 
inches in length having an iron wire in its axis, and this being 
employed in the apparatus gave the pure effect of the copper 
with its induced currents. Yet this core, as a whole, was 
highly magnetic to an ordinary test-needle; and when the 
two changes of the commutator were not equidistant from the 
one stop or the other (2670. 2677.), the iron eifect came out 
powerfully, overruling the former and producing very strong 
contrary deflections at the needle. The platinum core which 
I have used is an imperfect cylinder, 2 inches long and 0'62 
of an inch thick: it points magnetically between the poles of 

supposed Polarity of Dlamagnetic Bodies. 101 

a horseshoe electro-maivnet (2381.), making a vibration in less 
than a second, but with the above condition of llie commutator 
(2675.) gives 4° of deMcction (kie to the inchiccd currents, tiie 
magnetic effect beiuir annulled or thrown out. 

26S0. Some of the combined effects produced by obli(iue 
position of the commutator points were worked out in confir- 
mation of the forn)er conchisions (2677.). When the commu- 
tator was so adjusted as to combine any polar power which 
the bismuth, as a diamagnetic body, might possess, with any 
conducting power which would permit the fbrn)ation of cur- 
rents by induction in its mass (2676.), still the effects were so 
minute and uncertain as to oblige me to say that, experimen- 
tally, it is without either polar or inductive action. 

2681. There is another distinction which may usefully be 
established between the effects of a true sustainable polarity, 
either magnetic or diamagnetic, and those of the transient 
induced currents dependent upon tiinc. If we consider the 
resistance in the circuit, which includes the experimental helix 
and the galvanometer coil, as nothing, then a magnetic pole 
of constant strength passed a certain distance into the helix, 
would produce the same amount of current electricity in it, 
whether the pole were moved into its place by a cjuick or a 
slow motion. Or if the iron core be used (2668.) liie same 
result is produced, provided, in any alternating action, the 
core is lelt long enough at the extremities of its journey to 
acquire, either in its quick or slow alternation, the same state. 
This 1 found to be the fact when no commutator nor domi- 
nant magnet was used: a sinnle insertion of a weak maonetic 
pole gave the same deflection, whether introduced quickly or 
slowly; and when the residual dominant magnet, an iron wire 
core, and the commutator in its position «, b (2677.) were 
used, four journeys to and from produced the same effect at 
the galvanometer when the velocities were as 1 : 5 or even 
as T: 10. 

2682. When a copper, silver, or gold core is employed in 
place of the iron, the effect is very different. There is no 
reason to doubt that, as regards the core itself, the same 
amount of electricity is thrown into the form of induced cir- 
culating currents within it, by a journey to or from, v.hether 
that journey is performed quickly or slowly: the above expe- 
riment (2681.) in fact confirms such a conclusion. But the 
effect which is produced upon the experimental helix is not 
proportionate to the whole amount of these currents, but to 
the maximum intensities to which they rise. When the core 
moves slowly, this intensity is small; when it moves rapidly, 
it is great, and necessarily so, for the same current of elec- 

lO'J Dr. Faraday's Experimeiital Researches in FAcctricify : 

tricity lias to travel in the two differing periods of time occu- 
pied by the journeys. Hence the quickly niovinocore should 
produce a far hinrher effect on the experimental helix than the 
slowly moving core ; and this also I found to be the fact. 

2683. The short copper core was adjusted to the apparatus, 
and the machine worked with its average velocity until forty 
journeys to and from had been completed; the galvanometer 
needle passed 39^ west. Then the machine was worked with 
a greater rapidity, also for forty journeys, and the needle 
passed tiirough 80° or more west; finally, being worked at a 
slow rate for the same number of journeys, the needle went 
through only 21° west. The extreme velocities in this expe- 
riment were pi-obably as 1:6; the time in the longest case 
was considerably less than that of one vil)ration of the needle 
(2651.), so that I believe all the force in the slowest case was 
collected. The needle is very little influenced by the swing 
or momentum of its parts, because of the deadening effect of 
the copper plate beneath it, and, except to return to zero, 
moves very little after the motion of the apparatus ceases. A 
silver core produced the same results. 

2681'. These effects of induced currents have a relation to 
the phaenomena of revulsion which I formerly described 
(2310. 2315. 2338.), being the same in their exciting cause 
and principles of action, and so the two sets of phaenomena 
confirm and illustrate each other. That the revulsive phae- 
nomena are produced by induced currents, has been shown 
before (2327. 2329. 2336. 2339.) ; the only difference is, that 
with them the induced currents were produced by exalting 
the force of a magnet placed at a fixed distance from the 
affected metal; whilst in the present phaenomena, the force of 
the magnet does not change, but its distance from the piece 
of metal does. 

2685. So also the same circumstances which affect the 
phaenomena here affect the revulsive phaenomena. A plate of 
metal will, as a whole, be well-revulsed ; but if it be divided 
across the course of the induced currents it is not then affected 
(2529.). A ring helix of copper wire, if the extremities be 
unconnected, will not exhibit the phaenomena, but if they be 
connected then it presents them (2660.). 

2686. On the whole, the revulsive phaenomena are a far 
better test and indication of these currents than the present 
effects; especially if advantage be taken of the division of tlie 
mass into plates, so as to be analogous, or rather superior, in 
their action to the disc cylinder cores (2659. 2661.). Plati- 
num, palladium and lead in leaf or foil, if cut or folded into 
squares half an inch in the side, and then packed regularly 

supposed Polaritij of Diamagnetic Bodies. 103 

together, will show the pheenomena of revulsion very well: 
anil that according- to the direction of the leaves, and not of 
the external form. Gold, silver, tin and copper have the re- 
vulsive efi'ects tluis greatly exalted. Antimony, as I have 
already shown, exhibits the effect well (2514'. 2519.). Both 
it and bismuth can be made to give evidence of the induced 
currents produced in them when they are used in thin plates, 
either single or associated, although, to avoid the influence of 
the diamagnetic force, a little attention is required to the 
moments of making and breaking contact between the voltaic 
battery and the electro- magnet. 

2687. Copper, when thus divided into plates, had its revul- 
sive phaenomena raised to a degree that I had not before ob- 
served. A piece of copper foil was annealed and tarnished 
by heat, and then folded up into a small square block, half an 
inch in the side and a quarter of an inch thick, containing 
seventy-two folds of the metal. This block was suspended by 
a silk film as before (22'1'8.), and whilst at an angle of 30° or 
thereabouts with the equatorial line (2252.), the electro-magnet 
was excited ; it immediately advanced or turned until the 
angle was about 45° or 50°, and then stood still. Upon the 
interruption of the electric current at the magnet the revulsion 
came on very strongly, and the block turned back again, 
passed the equatorial line, and proceeded on until it formed 
an angle of 50° or 60° on the other side ; but instead of con- 
tinuing to revolve in that direction as before (2315.), it then 
returned on its course, again passed the equatorial line, and 
almost reached the axial position before it stood still. In fact, 
as a mass, it vibrated to and fro about the equatorial line. 

2688. This however is a simple result of the principles of 
action formerlj' developed (2329. 2336.). The revulsion is 
due to the production of induced currents in the suspended 
mass during the falling of the magnetism of the electro- 
magnet; and the effect of the action is to bring the axis of 
these induced currents parallel to the axis of force in the mag- 
netic field. Consequently, if the time of the fall of magnetic 
force, and therefore of tiie currents dependent thereon, be 
greater than the time occupied by the revulsion of the copper 
block as far as the equatorial line, any further motion of it 
by momentum will be counteracted by a contrary force; and 
if this force be strong enough the block will return. The 
conducting power of the copper and its division into laminae, 
tend to set up these currents very readily and with extra 
power ; and the ver}' power which they possess tends to make 
the time of a vibration so short, that two or even three vibra- 
tions can occur before the force of the electro-magnet has 

101- Dr. Faraday's Experimental Researches in Eleclriciljj :j 

ceased to fall any further. The effect of iimc^ both in the 
lining ami fallino; of powei", has been referred to on many 
former occasions (2170. 2G50.), and is very beautifully seen 

26S9. Uclurninq; to the subject of (he assumed polarity of 
bismuth, I r.)ay and oui>ht to refer to an experiment made by 
lleich, and described by Weber*, which, if I understand the 
instruction aright, is as follows: a strong horseshoe magnet 
is laid upon a table in such a position that the line joining its 
two poles is perpendicular to the magnetic meridian and to 
be considered as [prolonged on one side; in that line, and 
near the magnt-t, is to be placed a small [lowerful magnetic 
needle, suspentled by cocoon silk, and on the other side of it, 
the pole of a bar magnet, in such a position and so near, as 
exactly to counteract the effect of the horseshoe magnet, and 
leave the needle lo point exactly as if both magnets were 
awav. Then a mass of bismuth being placed between the 
poles of die horseshoe magnet is said to react upon the small 
magnet needle, causing its deflection in a particidar direction, 
and this is supposed lo indicate the polaiity of the bismuth 
under the circumstances, as it lias no such action when the 
magnets are away. A piece of iron in place of the bismuth 
produces the contrary deflection of the needle. 

2G90. I have repeated this experiment most anxiously and 
carefully, but have never obtained the slightest trace of action 
with the bismuth. I have obtained action vvitii the iron; but 
in those cases the action was far less than if the iron were 
applied outside between the horseshoe magnet and the needle, 
or to the needle alone, the magnets being entirely away. On 
using a garnet, or a weak magnetic substance of any kind, I 
cannot find that the arrangement is at all comparable for rea- 
diness of indication or delicacy, with the use of a common or 
an astatic needle, and therefore I do not understand how it 
could become a test of the polarity of bismuth when these fail 
to show it. Still I may have made some mistake; but neither 
by close reference to the description, nor to the principles of 
))olar action, can I discover where. 

2691. There is an experiment which Pl'iickcr described to 
me, and whic!) at first seems to indicate strongly the polarity 
of bismuth. If a bar of bismuth (or phosphorus) be suspended 
horizontally between the poles of the electro- magnet, it will 
go to the ecjuatorial position with a certain force, passing, as I 
have said, from stronger to weaker places of action (2267.). 

* Taylor's Scientific Memoirs, vol. v. p. 480. 

supposed Polaritif of Diamagnetic Bodies. 105 

If a bar of iron of the same size be fixed in the equatorial 
position a httle below the pUane in which the cliama<^netic bar 
is niovinjr, the latter will proceed to the equatorial position 
with much greater force than before, and this is considered 
as due to the circumstance, that, on the side where the iron 
has N polarity, the diamasrnetic body has S polarity, and that 
on the other side the S polarity of the iron and the N polarity 
of the bismuth also coincide. 

2692. It is however very evident that the lines of magnetic 
force have been altered sufficiently in their intensity of direc- 
tion, by the presence of the iron, to account fully for the in- 
creased effect. For, consider the bar as just leaving tlie axial 
position and going to the equatorial position ; at the moment 
of starting its extremities are in places of stronger magnetic 
force than before, for it cannot be tloubted for a moment that 
the iron bar determines more force from pole to pole ot the 
electro-magnet than if it were away. On the other hand, 
when it has attained the e(]uatorial position, the extremities 
are under a much weaker magnetic force than they were sub- 
ject to in the same places before; for the iron bar determines 
downwards uj^on itself much of that force, which, when it is 
net there, exists in the })lane occupied by the bismuth. Hence, 
in passing through DO", the diamagnetic is in"ged by a much 
greater difference of intensity of force when the iron is present 
than when it is away; and hence, probably, the whole addi- 
tional result. The effect is like many others which I have 
referred to in magnecrystallic action (24>87-24'97.), and does 
not, I think, add anything to the experimental proof of dia- 
magnetic polarity. 

2693. Finally, I am obliged to say that I can find no ex- 
perimental evidence to support the hypothetical view of dia- 
magnetic polarity (2640.), either in my own experiments, or 
in the repetition of tliose of Weber, Reich, or others. 1 do 
not say that such a polarity does not exist; and I should think 
it possible that Weber, by far more delicate apparatus than 
mine, had obtained a trace of it, were it not that then also he 
would have certainly met with tiie far raore powerful effects 
produced by copper, gold, silver, and the better conducting 
diamagnetics. If bismuth should be found to give an}' effect, 
it must be checked and distinguished by reference to the posi- 
tion of the commutator, division of the mass by pulverization, 
influence of time, &c. It appears to me also, that, as the 
magnetic polarity conferred by iron or nickel in very small 
quantity, and in unfavourable states, is far more readily indi- 
cated by its effect on an astatic needle, or by pointing between 
the poles of a strong horseshoe magnet, than by any such 

106 Dr. Faraday's Experimental Researches in Electricity : 

arrnn<rcnient as mine or Weber's or Reich's, so {liamagnetic 
jiolarity would be much more easily distinguished in the same 
way, and that no indication of that polarity has as yet reached 
to the force and value of those already given by Brugmann 
and niyself. 

2G94-. iSo, at present, the actions representeil or typified by 
iron, by copper and by bismuth, remain distinct; anil their 
relations are only in part made known to us. It cannot be 
doubted that a larger and simpler law of action than any we 
are yet acijuainted with, will hereal'ter be discovered, which 
shall incluile all these actions at once; and the beauty of 
Weber's suggestion in this respect was the chief inducement 
to me to endeavour to establish it. 

2695. Though iVom the considerations above expressed 
(2693.) I had little hopes of any useful results, yet I thought 
it right to submit certain niagnecrystallic cores to the action 
ot the apparatus. One core was a large group of synmietri- 
cally disposed crystals of bismuth {2-^51.); another a very 
Jarge crystal of red ferroprussiate of potassa ; a third a cry- 
stal of calcaieous spar: and a fourth and fifth large crystals 
of protosulphate of iron. Tliese were formed into cylinders, 
of which the first and fourth had the magnecrystallic axes 
(24'79.) jiarallel to the axis of the cylinder, and the second, 
third and fifth, had the e(]ualorial direction of force (2594. 
2595. "^5^6.) })arallel to the axis of the cylinder. None of 
them gave any effect at the galvanometer, except the fourth 
anil fifth, and these were alike in their results, and were de- 
pendent for them on theii" ordinary magnetic property. 

2696. Some of the expressions I have used may seem to 
imply, that, when employing the copper and other cores, I 
imagine that currents are first induced in them by the domi- 
nant magnet, and that these induce the currents which are 
observed in the experimental helix. Whether the cores act 
directly on the experimental helix or indirectly through their 
influence on the dominant magnet, is a very interesting ques- 
tion, and 1 have found it difficult to select expressions, though 
I wished to do so, which should not in some degree jirejudge 
that question. It seems to me probable, that the cores act 
indirectly on the helix, and that their immediate action is 
altogether directed towards the dominant magnet, which, 
whether they consist of magnetic or diamagnetie metals, raises 
them into power either permanently or transiently, and has 
their power for that time directed towards it. Before the 
core moves to approach the magnet, the magnet and experi- 
mental helix are in close relation ; and the latter is situated 
in the intense field of magnetic force which belongs to the 

supposed Polarity of Diamagnetic Bodies. 107 

pole of tl)e former. If the core be iron, as it approaches the 
majjiiet it causes a strono- convergence and concentration of 
the lines of magnetic force upon itself; and these, as they so 
converge, passing through the helix and across its convolu- 
tions, are competent to produce the currents in it which are 
obtained (2653. 2668.). As the iron retreats these lines of 
force diverge, and again crossing the line of the wire in the 
helix in a contrary direction to their former course, produce a 
contrary current. It does not seem necessary, in viewing the 
action of the iron core, to suppose any direct action of it on 
the helix, or any other action than tiiis which it exerts upon 
the lines of force of the magnet. In such a case its action 
upon the helix would be indirect. 

2697. Then, by all parity of reasoning, when a copper core 
enters the helix its action upon it should be indirect also. For 
the currents wliich are produced in it are caused by the direct 
influence of the magnet, and must react equivalently upon it. 
This they do, and because of their direction and known action, 
they will cause the lines of force of the magnet to diverge. As 
the core diminishes in its velocity of motion, or comes to rest, 
the currents in it will cease, and tlien the lines of force will 
converge ; and this divergence and convergence, or passage in 
two directions across the wire of the experimental helix, is 
sufficient to produce the two currents which are obtained in 
the advance of the core towards the dominant magnet (2671. 
2673.). A corresponding effect in the contrary direction is 
produced by the retreat ot the core. 

2698. On the idea that the actions of the core were not of 
this kind, but more directly upon the helix, I interposed sub- 
stances between the core and the helix during the times of the 
experiment. A thick copper cylinder 2*2 inches long, 0'7 of 
an inch external diameter, and 0*1 of an inch internal dia- 
meter, anil consequently 0'3 of an inch thick in thesitles, was 
placed in the experimental helix, and an iron wire core (2668.) 
used in the apparatus. Still, whatever the form of the expe- 
riment, the kind and amount of effect produced was the same 
as if the copper were away, and either glass or air in its place. 
When the dominant magnet was removed and the wire core 
made a magnet, the same results were produced. 

2699. Another copper lining, being a cylinder 2*5 inches 
long, 1 inch in external diameter, and one-eighth of an inch 
in thickness, was placed in the experimental helix, and cores 
of silver and copper five-eighths of an inch in thickness, em- 
ployed as before, with the best condition of the commutator 
(2675.): the effects, with and without the copper, or with and 
without the glass, were absolutely the same (2698.). 

108 Mr, W. Spottiswoode uii the Geometrical 

2700. There can be no tloubt that the copper linings, when 
in phico, were lull oJ currents at the time of action, and that 
w hen away no sncii currents would exist in the air ov glass 
replacing iheni. There is also full reason to admit, that the 
diverjrence and convergence of the magnetic lines of force 
sujiposed above (2697.) would satisfactorily account for such 
currents in them, supposing the indirect action of the cores 
were assumed. If that supposiiii)n be rejocteil, then it seems 
to me that the wlu)le of the bodies present, the magnet, the 
helix, the core, the coj)per lining, or the air or glass which 
)eplaces it, must all be in a state of tension, each part acting 
t)n every other part, being in what 1 have occasionally else- 
where imagined as the electro-tonic state (1729.). 

2701. The advance of the copper makes the lines of mag- 
netic force diverge, or, so to say, drives them before it (2697.). 
No doubt there is reaction upon the advancing copper, and 
the production of currents in it in such a direction as makes 
them competent, if continued, to continue the divergence. But 
it does not seem logical to say, that the currents which the 
lines of force cause in the copper, are the cause of the diver- 
gence of the lines of force. It seems to me, rather, that the 
lines of force are, so to say, diverged, or bent outward by the 
advancing copper (or by a connected wire moving across lines 
of force in any other form of the experiments), and that the 
reaction of the lines of force upon the forces in the particles 
of the copper causes them to be resolved into a current, by 
which the resistance is discharged and removed, and the line 
of force returns to its place. I attach no other meaning to 
the words line of force than that I have given on a former 
occasion (214'9.). 

Royal Institution, Dec. 14, 1841). 

X. On the Geometrical Interpretation of Qiiaternions. 
^j/WiLLiAM Spottjswoodi:, M.A., (f Balliol College^Oxford^''. 

§ 1 . Fundamental La'jcs. 

THE following investigations refer to the same subject as 
that treated by Professor Donkin in vol. xxxvi. of this 
Journal; and are offered, not as at all preferable to his, but 
simply as indicating another mode in which the question maybe 
viewed ; it being desirable to exhibit a subject, which is some- 
what new, in more than one way, in order that as much light 
as possible may be thrown upon it. The {iresent paper will be 
interesting (if it is so at all) principally because its results are 
substantially the same as those of the pajier just referred to, 
* Comnuinicalcd bv tlie Author. 

Interpretation of Qiiaternions. 109 

althougli obtained by uii entirely independent process. I have 
stated my views as briefly as possible, becanse Prof. Donkin's 
paper renders any more lengthened discussion superfluons; 
and if any expressions occur which appear to indicate a view 
o( algebraic f^ymbols, Sec. different from his, they have been 
used merely because they are the ordinary terms ; and 1 should 
wish them to be understood as far as possible in his way, if 
for no better reason, at least in order that the two methods 
may be compared. 

The calculus of (juaternions is a generalization of algebra, 
in which sets of four ordinary algebraical quantities are used 
instead of single quantities. Each such set of four quantities 
is called a (juaternion ; the nature and laws of combination of 
which are the object of the jiresent investigations. The cor- 
responiiing laws in ordinary algebra will be assumed as known. 

Let a quaternion be defined to be a set of four algebraic 
(juantities consillered with reference to their order of position, 
and let it be expressed by the following equation, 

Q = {'ix, X, y, z), (1.) 

in which Q, or its equivalent, is called the quaternion, and 
w, A', J/, z its constituents. As this definition involves no law 
of connexion between the constituents, it is clear that the equi- 
valence of any number of quaternions must involve the equi- 
valence of tlieir several constituents; so that the equations 

Q = Qj = Q2= (2.) 

involve the following, 

' - > (3.) 

and conversely (3.) will involve (2.). The same principle 
gives rise to the following law for the addition and subtraction 
of quaternions: 

SQ; = (St.„, 2.-,,, %„, 2. J; .... (4.) 

particular cases of which are 

7iQ = {?rji'', nx, nj/, nz) (5.) 

Q-Q = 0=(0, 0, 0, 0) (G.) 

The following consideration will assist turtlier investigations. 
The qiiaternion 

(w, 0,0,0) (7.) 

is a system consisting of the quantity vo, followed by no other 

1 10 Mr. W. Spottiswoode on the Geometrical 

quantities, i. c. associated with iiothiiifT but itself; in other 
words, it is simply ec|uivalent to the ortiinary algebraic (pian- 
tity w; so that by means of the law of addition ol' quaternions, 
it will be allowable to write, 

(tcvv,j/,.i = (w,0,0,OH(Ov'',0,0)-[-(0,0,^,0) + (0,0,(),^)Kg 
= w+(0,a-,0, 0) + (0,0,i/, 0) + (0,0, 0,2) J 

With respect to the last three terms of this expression, it will 
be necessary to introduce some new symbols. Thus, for in- 
stance, if T, T', T" indicate the ojierations of transposition 
defined by the following equations, 

T (.r,0, 0,0) = (0,.r, 0,0)1 

T'(.y,0, 0, 0) = (0,0,,7/,0) j>, . . . (9.) 

T" (2, 0,0,0) =(0,0, 0,2) J 

the equation (S.) might be written 

Q = w + 1> + T'j/ + T"s. .... (10.) 

And, if the laws of the combination of the symbols T, T', T" 
were known, the general laws of the combination of quater- 
nions would be at once deducible. 

It will however be more advantageous to use some symbols 
of transposition rather different from those above noticed ; let 

iQ = { — x, 'w,—z,i/) ^ 

from these definitions of the symbols of transposition, /,jf k, 
it is easy to deduce the following relations: 

i.iQ=J.JQ=k.kQ = i.J.kQ = {— w, — .r, -i/, -~)= -Q] 
k.iQ = -iJcQ=jQ 

i.jQ=-j.iQ=m J 

in which the expression for — Q may be deduced from (.5.) by 
writing — 1 for ?h These relations may be symbolically 
written, as follows: 




jk=-kj = i I 

/ci= —ik=j [ 

Interpretation of Quaternions, 111 

the operations of transposition and change of sign being in- 
tlependent of the subject of operation. 

As it will assist the geometrical interpretation of the ope- 
rations i,J, k hereafter, to sejiarate each of them into two di- 
stinct operations, the formulae to which such separation gives 
rise may be properly noticed here. Let then 

i'Q={- X, IV, y, z) i"Q = ( ot, x, — z, jy)l 
J'Q= i-JJ, ^v, 'iv, z) /Q= (w, z, y, -.V) I ; (14.) 
/,'Q ={-z, .r, J/, iv) k"Q = (w, -J/, .1', .::; ) J 
there will then result 

i = i' i" = i" i ~\ 

j=j'f=fj' \. (15.) 

to which may be added, 

i"j'=kH\ fk' = i'j\ kH'=j'h'\'\ 

fJi^'=k'^i!' = i"j" L . . (16.) 

V(iiH") = Fijj'j") = P{kk'k") = - 1 J 

where P represents the symbolical product without reference 
to order. By means of the above properties of i,j. k, it will 
be possible to transform the expression of a quaternion (1.) 
into another of the same form as (10.) ; for 

(0, X, 0, 0) = / (.r, 0, 0, 0) =/.r ~| 

(0, 0, ij, 0) =;• (j/, 0, 0, 0) =iy I ; . . (17.) 

(0, 0, 0, ^) = %, 0, 0, 0)=/^^J 

so that (8.) may be written thus, 

Q-w + i^v+ji^ + kr:, (18.) 

in which i,j, k may be combined according to the laws de- 
fined l)y (13.). It may be observed, that, since by means of 
the condition (4.) the addition of quaternions is reduced to the 
addition of ordinary algebraical quantities, the order and clus- 
tering of the terms in (18.) is indifferent, so that the associa- 
tive pri?iciple of addition among those terms is completely 
established ; the same is obviously the case with respect to 
the addition of quaternions in general. It may be further 
remarked, that, since by means of (4.), 

^■SQ,=2/Q,, jtQ=V^^, A-SQ„=2/1-Q„~1 

jkX(^=^jkQl,, kiXQ=^kiQ^^, ijl^Q=^ijQl, (19.) 

=i2A"Q„ =:/:S.-Q„, =/S;-qJ 

112 Mr. \\'. Spotti^uoode on llic Geometrical 

with other like tbnmiho, ///(• (lisfyibniive character of the sym- 
bols i,j, k is also established. 

The followini^ verifications, although not essential to the 
theory, are perhaps worth noticing. If we had taken (IS.) as 
the definition of a (juaternion with (13.) as the definitions of 
i,j, k, we should have found 

/U = ? to — X + ky —jz 1 

jQ=jxo-kx-ij-^iz I; . . . . (20.) 

A-Q = kw +J.V — ii)—'.} 

so that the equations 

Q = Qi-Q>=..., 

which obviously involve also 

iQ=7Qi=;Q.= -. >, .... (21.) 

A-Q = A'Q, = /tQ,= ...J 

give rise to the equations (3.) ; for /, J, k being- symbolical ex- 
pressions for (— )*, render all real terms, to which they are 
prefixed, imaginary in the ordinary sense of that word. The 
same definition of a quaternion gives 

2Q,=Stc;„ + /Sa.„+i2//„-hyt2~v . . . (22.) 

which is in fact identical with (4.). 

But the principal advantage of the linear form of the ex- 
pression for a quaternion is found in the processes of multipli- 
cation and division. In the form (1.) it does not seem possible 
to obtain a complete solution of the problem of multiplication ; 
the following however would be the initial steps to such a 
solution : 

Q . Qi = (w, .r, j/, z) . (u'i, n\, i/i, z^) 
= {w(Wi,a-i,j/i,z,), .r(Wi,.ri,j/„z,), i/{Wi,x^,7/y,z^), ^(TO„.ri,j/„,^,)} 
= {TO(Wi,.ri,j/„^,), 0,0,0} 
+ {0, a,'(tui, .r],?/,,;^,), 0, 0} 
+ {0, 0,,7/(M„a'i, y„2;,), 0} 
+ {0,0,0, z{w^,a,\,y^,^^)} 

=^{w^'w, w^x, iso^y, xio^z) 
+ {0, .rti'i + .r(0, a'l, 0, 0) + x{(), 0, ^„ O) +.^ (O, 0, 0, ,-.,), 0, 0} 
+ {0, 0,3/w,+y(0, x„ 0, 0) +j/(0, 0, j/i, 0) +j/(0, 0, 0, z,), 0} 
+ {0, 0, 0, zu\ + z[0,x,, 0, 0) +s(0, 0,y„ 0) +^(0, 0, 0, ^,)} 


Interprelatioii of Qtiateniiotis. 113 

= (tt)t<yi, U',.r + .riW, i<o^ij-\-y{-jo, li-^z ■\- :: {tso) 
+ (0,.r,.?/,.-).(0, .r„0, 0) 
+ (0,.r,.y,^).(0,0,j/i,0) 

But if we adopt the form (18.), the constituents of" the product 
of two quaternions are completely determined ; in ihct, it is 
found without ilifficulty that if 

ttio = TOW, — XX ^ —}Jl)x ~ ~^1 "^ 

.1-2= m-, + w,a; \yz^ -xj^z 

;ro = to:; 1 + TOjS + ^^1 - .r 1 j/ J 
And also, if 

Q,Q = Q,i = TO2i4-«>2'+i/-2' + '^^^V. • • • (26.) 

TOo = toJ, .1-2=— .rsS ?/o=— y'2^ -2=— -2*- • (27-) 


(2a;+j-^ + /^z)2=-a.-2-/-22 .... (28.) 

Q2=tu2_^2_^2_^2^2w(/^-|-J'> + A-.'i) . (29.) 

(to — ix —jy — /:.:■) (to + ix +Jy + kz) = to^ + x" +y'^ + z~ ' 

= (to + ix +jy +kz){w — tx —jy — k. 

So that the reciprocal of a quaternion is the quotient of the 
quaternion itself, with the signs of its last three constituents 
changed divided by the sum of the squares of the constituents. 
The constituents of the ratio 


may be found either by solving (25.) with respect tow,, a,, t/,, z^^ 
or by means of the relatio.n (30.), and so reducing the division 
to multiplication, 

§ 2. Geometrical Interpretation. 

In the general expression 

Q = ( TO, X, y, 2;) = to + ix +jy + Jcz, . . . ( 1 . ) 

let TO, a-, y, z represent straight lines drawn in several direc- 
tions from the origin, and let x, y, z coincide with the three 
positive axes of coordinates respectively, while the direction 
of TO is arbitrary ; x, y^ z may then be considered as the co- 
ordinates of some point, in general not the extremity of w. 
P/iil. Mag. S. 3. Vol. 37. No. 248. August 1850. ' I 


114 ISIi". W, Spottiswoode on the Gcomclrical 

In accordance with the fundamental idea of a quaternion, the 
position of the line represented by any constituent will be sup- 
posed to depend upon the })osition which that constituent 
holds in the first expression for Q; so that the directions of 
the ibur lines bcino- once chosen, the first, second, third, and 
fourth constituents will always represent lines drawn in the 
four directions respectively, whatever changes may have taken 
place in the order of the constituents as originally given. Now, 
returning to the equations (L'5.) and (I't.) of the former sec- 
tion, it appears that 2" indicates a change by which the nega- 
tive axis of::: is brought into the old j)osition of the axesof ?/; 
and the axis of y into the old position of the axis of 2; the 
positions of w and x remaining unchanged ; or i" may be con- 
sidered as indicating a change by which to and x are brought 
into positions such, that they are situated, with respect tot he 
negative axis of -r and the positive axis of j/, in the same man- 
ner as they were at first with respect to the axes of j/ and z 
respectively. When the axes are rectangular, as at present, 
this change may be represented, either by supposing the plane 
o\yz to revolve in its own plane through half a right angle in 
the direction from y to ;:■, or by supposing the three axes to 
remain fixed, and the radius vector w to revolve on the surface 
of a right cone with a circular base, whose axis is that of x 
and vertex the origin, through one quarter of a revolution; 
the direction of rotation being from the axis of z towards that 
of J/. It is easily seen that j" and /^" may be represented by 
similar revolutions about the axes of?/ and z respectively. 

Again, i' indicates a change by which the negative axis of 
X is brought into the old position of to, and 'w into the old 
position of the positive axis of .r, the positions of ?/ and z re- 
maininfr unchanged ; and if a be the anjile between the axis 
of ^r and the line 10 (the vertical angle of the first cone), this 
change may be represented by bringing the negative axis of 
the cone into the old position of w, and then opening the ver- 
tical angle of the cone through an angle =7r— 2a. The 
changes j' and k' may similarly be represented by supposing 
the negative axes of the other two cones respectively to take 
the position of w, and the vertical angle of the cones to be 
opened through angles =7r — 2/3and 7r—2'y respectively. The 
above theory becomes much simpler when the position of TO is 
not absolutely determined, but merely restricted to a given 
plane ; in this case its position may be supposed to coincide 
with the intersection of that plane with one of the coordinate 
planes ; e. g. in the case of i, with the intersection with the 
plane of j/z ; in that oi'j, with that of zx ; and in that of X-, with 
that of a,'7j; the three cones then become simply the three co- 

Interpretation of Qtiaternio7is. 1 1 5 

ordinate planes, and i",/', k" will represent rotations of this 

line of intersection through angles = - in the planes of ^2", zx, 

xy respectively; and ?',/, Z:' similar rotations in the planes of 
lax^ ixy^ "wz. In each case the origin of the rotations is deter- 

If the position of w be entirely arbitrary, the positions of 
the intersections of the planes of Wc*", tt.;y, ws with those ofj/.r, 
zx^ xij^ will be so also ; and the only difference arising in the 
significations of i\j\ A', z",/', /", will be that the origin of 
rotation is restricted only to the three coordinate planes suc- 
cessively, the position in those planes being arbitrary. These 
considerations will enable us to interpret the various terms in 
the linear expression for Q; for 

?-r = /(.r, 0, 0, 0) = (0, .r, 0, 0) .... (2.) 

j-i/^JCi/.o.o, 0) = (0, 0,j/, 0) .... (3.) 

/■;; = %,0,0,0)=(0, 0,0,;s) .... (4.) 

Now the first constituent of the quaternions on the right- 
hand side of the above expression will, according to the prin- 
ciples of interpretation above given, be considered as repre- 
senting a line coinciding with the intersection of a plane pass- 
ing through the axis of 

.X', with the plane of j/^", in (2.); 

y» S'*"? ••• (3.); 

-5 xy, ... (4.); 

and consequently ix^jy, kz will represent that the lines whose 
lengths are represented by .r, j/, z have revolved through 

angles each = ^ in planes perpendicular to their original di- 


Adopting the above interpretation of the various terms in 
the expression for a quaternion, the question next arises, in 
what sense are the lines represented by these terms, and by 
quaternions generally, said to be added ? Now the funda- 
mental formula for the addition of quaternions shows that in 
whatever way the line Q is formed from the quantities w^x,!/, z 
(with similar expressions for any other quaternions Qj, Q^ . .), 
then the sum — Q,, is a new quaternion line formed in the same 
manner from the quantities 2r^,, S.t;^, 2j/,^, S^'^ ; and writing • 

2;Q„=<SI=(W, X, Y, Z), 

it appears that W will be the algebraical sum of the lines 
w?, tiUj, . . , supposed, for convenience, to be similarly directed, 


116 Ml". ^^^ Spottiswoodo on the Geometrical 

and X, Y, Z will be the coordinates of the extremity of the 
diagonal ot the parallelopiped formed on the sums of the com- 
ponent coordinates as its edges. From these two facts it a|)- 
peurs that straight lines lying in the same straight line are to 
be adtied as in oidinaiy algebraical geometry, while the sum 
of any other set of straiglit Mnes inclined to one another at any 
angles is the closing side of the polygon formed by placing 
the beginning of eacli line at the termination of its jirede- 
cessor. In fact, lines arc to be added as forces are equilibrated 
in statics. In accordance with this principle, tiie sum 

ix +jy + 1:^ 

will represent the diagonal of tlie parallelopiped described on 
the line i.Vyjy, kz as its edges; and since moreover 

therefore also 

ix-\-jij + J:.::={-)h; (5.) 

wliich, according to the principles of the present calculus, re- 
presents not merely a line in a plane perpendicular to r, but 
a line which has been brought into its position by means of a 

rotation through an angle = - in that plane ; or, in otlier 

words, about an axis whose direction-cosines are x\r, y. r, 
Z'.r; and finally, the sum 

w + w'+jjZ + Zs 

will represent the diagonal of the square whose sides are 

(these two lines being obviously perpendicular). The length 
of the whole line is consequently 

(toVA>^-+i/^- + ^^f = F' (6.) 

and its direction makes an angle, whose tangent is =7:w, 
with the direction of tu; the whole quaternion will therefore 
represent a line whose length is p, which has been turned 
through an angle = tan~'(?:w) in the plane, the direction- 
cosines o'i whose normal are x :r, y:r, z : r. The expres- 
sion (1.) may also be written as follows: 

{cos 5+ sin (//+>? + /vi) }p, .... (7.) 

6= tan~'(r : to) 
X : l—y. m = z : ?? = 

.,.}.... (8.) 

Interpretation of Quaternions. 117 

Tlie following cases will exemplify the above interpretation 
of quaternions. 

If ABC be a spherical triangle, the radius being equal to 
unity, and if Q, Q', Q" indicate the rotations of the radius 
vector from B to C. from C to A, from A to B respectively, 
it is clear that we must always have 

Q"Q'Q = QQ"Q' = Q'QQ" = 1 . 

In order to find the quaternion which will represent the ro- 
tation from the line (/, m, ?i) to the line (/', ?«', «'), we may con- 
struct a ()uadrantal triangle such that (/, ??/, ?/), (/', m'^ n'} pass 
through the angles opposite to the quadrantal sides ; and if Q 
be the required quaternion, 

(// + 7nJ + nk) [I'i + m'j + n'/:) Q = — 1 ; 
but since 

{li-\-mj + n/ij'= {I' i + m'j + n' k)- = — 1, 

{I'i + mj+n'/c)Q = {li + mj-\- n/,) 

— Q = {I'i + 7n'j + n'/c) {li + mj + nk) 

Q= —(^ll'^mm' + 7in')+i{m?i' — m'?i) +j{rd' -7i'l) + k{lm' — I'm). 

To find the (juaternions which will represent the rotations 
from the three coordinate axes to the line (/, m,ii), we need 
only put in the above equation, 

wj = 0, 71 = 0', n = 0, Z=0: ^ = 0, m = 

in succession; hence, dropping the accents, 

Q^=—l—jn + Am 

Q,y=—m + in — kl 

Q^=—n — ivi+jl.; 

to which may be added the following relations : 


^'Q^, +jQ^ + kQ^—— il —jm — kn 

nQ^—mQ,^ = i — l{il+jm-\-kn) 

lQ^ — nQ^=:j—7n{il+jm -f kn) 

7nQ^,—lQ =k — 7i{il+j7n-\-kn) 

{jm-k7i)Q^.+ {in-/cl)Qy + {jl-i?n)Q^=-2 

= {nQ^-7nQf+ {lQ^-.7iQJ^+{77iQ-lQ/-. 

118 On the Geometrical Interpretation of Quaternions. 
If Q, Q', Q" be any quaternions, the condition 
aQ + /3Q' + 7Q" = 

is equivalent to the system 


from the last three of which may be deduced 

X, x', x" =0 

2/> y\ y" 

which is the condition that the three lines, whose direction- 
cosines are proportional to .r, ?/, z, ..., lie in the same plane ; 
in other words, the planes of rotation of the three quaternions 
are all parallel to one straight line. 

If Q, Q', Q" represent the rotations BC, CA, AB of the 
spherical triangle ABC, the quaternions 

aQ"-7Q = Q2 

/3Q-«Q' = Q3 

will represent arcs drawn from the angular points A, B, C, 
and cutting the opposite sides in points whose segments are in 
the ratios (3 :y, y. a, a: jS respectively, and the resulting con- 

«Qi-f-/3Q2 + yQ3 = 

shows that the three planes of rotation intersect in a common 
line, for they all pass through the same point, viz. the centre 
of the sphere ; consequently the three arcs all meet in a point. 

the points where the arcs Qj, Qg, Q3 meet the sides of the 
triangle will be the middle points of those sides, and the con- 

Qi + Q2+Q3=o 

will express that the three arcs meet in a point. This theorem 
includes all the corresponding theorems with respect to plane 

[ 119 ] 

XL On the Structure and Arrangement of the Tessera in a 
Roma?i pavement discovered at Cirencester in August 1849. By 
James Buckman, F.L.S., F.G.S* 

THE object of this paper is to point out the nature of the 
materials of which the party-coloured floors so beautifully 
^VT0ught in ancient Roman dwellings are composed, as also to 
offer some remarks upon their principles of arrangement. 

The tesserae of Roman pavements may be said to be formed 
out of two classes of materials, the first of which, consisting of 
portions of various coloured rocks, may be termed natural ; the 
second, of stained or coloured terra cottas and glass, being arti- 

The natural tesserse furnish but few colours, and those of a 
sober cast, hence these will be found forming shadings to figures 
entering largely into the composition of borders, or filling up the 
groundworks of the designs. They consist of portions of natural 
rocks from various localities, those belonging to the district where 
the pavement is found, as far as I have observed, always contri- 
buting their share. 

The Cirencester pavement presented the following : — 

Colours. Rocks. 

1. White, composed of Hard fine-grained Oolite. 

2. Light yellow Pebbles of the Wiltshire Drift, and Oolite. 

3. Gray The same as No. 1, altered by heat. 

4. Slate colom" or black ... Limestone bands of the Lower Lias. 

No. 1 occurs as a bed of compact fine-grained stone of about 
2 feet thick in nearly all the freestone quarries of this district, 
where it is distinguished under the name of the Limestone bed ; 
its geological position is about the middle of the freestone rocks 
of the Great Oolite ; it is well exposed at Trewsbury quarry, at 
the Acman Street Station, and at the smaller Sapperton tunnel, 
and was no doubt obtained by the Romans from the quarries 
once worked by them in the vicinity of the Querns. 

2. The tesserse, of a yellowish or nankeen hue, appear to 
have been made of portions of the pebble-drift with which parts 
of the neighbourhood of Cirencester is so thickly strewn. Stray 
pebbles of this may be found in almost every field to the south 
of the town, whilst at Somerford Kajoies, and other places, it en- 
ters largely into the composition of the gravel beds which are 
there worked. It is probable that this drift is the debris of that 
tertiary rock known in Wiltshire as Sarsen stone, of which the 
huge stones of Abury Camp constitute the more enduring mo- 

3. This, though differing so much in colour from No. 1, yet 

* Read to the Cotswold Club, Jan. 22, 1850. 

I'JO Mr. J. Buclunaii on the Slnuiutc and Arramicmoit 

seemed so identical in lithological structure as to induce me to 
try to ascertain from experiment whether or not they were the 
same, uhcn, on roasting; a portion of the rock No. 1 in the tire 
for a few minutes, it gradually assumed the colour of the gray 
tesscnc, the change no doubt being due to some alteration in the 
chemical conditions of the iron with which the stone is slightly 

4. The dark colour of the lias entered largely into the compo- 
sition of these pavements, as much of the outline of the design 
and the darker bands of the border ornaments are composed of 
this stone, which., judging from an Ammonite found in one of the 
tcsseric, was obtained from some one of the thin layers of argil- 
laceous limestone with which the clay-beds of the third division 
of the lower lias in the vale of Gloucester are separated, and no 
doubt the stone in question was brought from that locality. 

The artificial tessera found at Cirencester entered for the most 
part into the construction of the tiner and more important parts 
of the details of the figures and designs ; they consist of — • 

Colour. Substance. 

1. BliU'k 1 

2. Light red I Terra cotta or baked clay. 

3. Dark red J 

4. Brilliant rub)-red ... Glass. 

1 . This is a much darker shade than that of the lias, and Avas 
consequently used in those portions of figures where bold relief 
was required ; it seems to be composed of a dark-coloured clay, 
only slightly, if at all burnt ; as the tessera? are very fragile, this 
would almost lead to the conclusion that these were not arti- 
ficially coloured but made of a clay containing a large quantity of 
protoxide of iron, which is black, and they were consequently 
burnt in smother kilns, or the black would change to red by the 
protoxide becoming pcroxidized. The identity of constitution of 
these tesserpe with black pottery is very apparent. 

2 and 3. The two reds are made from clays containing more 
or less of iron, and perhaps this substance may have been added 
in these and in the instance above noticed, where it was desirable 
to deepen the tint ; of course the red is due to the peroxidation of 
the iron salts. 

4. In only one medallion of the Cirencester pavements has 
glass been made to play a part, and that is just when the trans- 
parency and brilliancy of colour of this substance were of the 
utmost importance to the composition. 

An examination of the pavement itself will show that the me- 
dallion which symbolized Spring, represents a fine female head 
crowned by what appears a chaplet of olive-green and verdigris- 
coloured leaves. Now on studying this head attentively, I w^as 


of the Te&sercc in a Roman Pavement. 121 

surprised at seeing these two colours intemiLxecl apparently in a 
most inharmonious manner; and as the verdigris-green was so 
different from any other colour I had met with, it suddenly 
struck mo that it was a mere coating to the tesserfe, resulting 
perhaps from chemical decomposition, and on scraping the sur- 
face with a knife I was gratified to find that the verdigris only 
covered up a glass of an exceedingly rich ruhy tint. I then ob- 
tained a small portion for a chemical analysis, which was kindly 
undertaken for me by Dr. Voelcker, the College Professor of 
Chemistry, the results of wliich arc so interesting that I must 
beg to lay it before the Club in his own words. 

Examination of red-coloured Roman glass {Cirencester). 

" The red glass which had undergone a partial decomposition 
was coated with a white crust, which itself was covered with a 
green substance. The latter on examination proved to be car- 
bonate of copper ; the white crust dissolved with effervescence 
in nitric acid, leaving gelatinous silicic acid behind, and was 
found to consist principally of carbonate of lead and silica. The 
glass, after having been treated with nitric acid and thus been 
deprived of the white and green coatings, exhibited a bright red 
colour ; it was now transparent, not very hard, and easily flexible 
when exposed to a moderate heat. On analysis the following- 
substances were detected, as — 

Oxide of lead. Oxide of iron. 

Protoxide of copper. Lime. 

Alumina. Silica. 

" The red colour of the glass undoubtedly is due to protoxide 
of copper, which was present probably in combination with alu- 
mina in considerable quantities. It is well known that the an- 
cients were acquainted with the art of colouring glass red by 
means of copper, for Cooper informs us (Annales de Chimie, 
serie 1. tom. Ixxiii. p. 20) that he detected in an antique red 
glass protoxide of copper, and Klaproth likewise ascribes the red 
colour of an antique glass to the presence of copper, which he con- 
siders to be contained in the glass in the state of protoxide. This 
gentleman found exactly the same constituent parts as those 
found by me in the Cirencester glass ; it has further been ascer- 
tained that all the red glass in antique mosaic church windows is 
coloured red by copper. Gold, which likewise imparts a beau- 
tiful red colour to glass, is never met with in Roman glass, and 
it appears that the property of gold and its combinations was 
unknown to the Romans, for we do not find any traces with the 
ancients which could justify the supposition of their being ac- 
quainted with the art of making the purple and rose-coloured or 

1 22 On the Arrangement of the Tessercc in a Roman Pavement. 

ruby-glass which at jiresent is manufactuvod in great perfection 
in Bohemia, where a prejjaration of gohl, generally chloride of 
gold, is used for tiiat ])urposc by the glass manufacturer. The 
ai)i)lication of gold jireparations in the ))reparation of red glass, 
comparatively speiiking, is of recent origin, for it appears that 
before the 17th century the use of gold pi'e])aration for this ])ar- 
ticular puri)osc was unknown. In the 17th century wc find 
the first reference made to the use of gold for colouring glass 
red by Cassius, who discovered and recommended a new com- 
bination of gold, which, to the present day, is known under the 
name of Cassius gold purjjle. 

" Coj^per thus ajjpears to have been the material with which 
the ancients were in the habit of colouring glass red. Various 
methods of a})plying copper were in use, and though metallic 
copper is capable of imbuing glass with a red colour, no doubt 
on account of the protoxide of coj^per which is found in almost 
every sample of copper, in most cases it was first subjected to 
o])erations which tended to generate protoxide of copper. Fre- 
quently also peroxide of coj)per (black oxide) was used for the 
same purpose, but in this case the glass mass received an addi- 
tion of substances, as tartar, charcoal, soot, ii*on, protoxide of 
iron, which substances at a red heat combine with part of the 
oxygen of the black oxide, and thus become the means of redu- 
cing the latter to red oxide of copper. 

" This important action of iron seems to have been known to the 
ancients, for both Cooper's and Klaproth's analyses of antique red 
glass referred to above, as well as my own of the Roman glass 
found in Cirencester, exhibits, besides oxide of copper, oxide of 
iron. Later the art of colouring glass red by means of copper 
was lost entirely, and many })ersons of om' days even denied 
altogether the possibility of producing a red glass with cojiper. 
Very generally all rod glass w'as supposed to contain gold. 

" The im])ortance of the subject induced the Society of Arts 
of Berlin to offer a prize for a method of manufacturing red glass 
by means of copper. The prize was gained hy D. Engelhardt of 
Zinswider, who gave several directions of manufacturing red 
glass, and who succeeded in making a beautiful red glass with 
protoxide of co])per and without using gold at all." ( Vide Ve?'- 
handl. des Gewerbevereins, Berlin, 1828, S. 15.) 

From this analysis it will be seen that the liomans imparted 
this red tint to glass by a very ingenious method, and it was the 
substance used for this purpose, namely copper, which covered 
over the tesserse as the surface of the glass had become decom- 
posed in the form of a carbonate of that metal. 

This fact is curious in its bearing upon the pavement as a work 
of art; as so harmoniously are the colours arranged in all the 

Effect ofPresmre in Lowering the Freezing-Point of Water. 1 23 

figures that it may almost be tal<cn for granted that, as in this 
instance, when there is an exception in this particular, it is due 
to some subsequent change having taken place in one or other 
of the colours. In the case before us our first tracing was co- 
loured with the verdigris-green : it was unsatisfactory ; but on 
making a new tracing and colouring it according to our amended 
observations, it at once became harmonious in colour, and as- 
sumed an intelligible form, though all our colouring will not 
enable us to convey the idea of ruby-gennned flowers like the 
substance used, the transparency of glass contributing much to 
the general effect. 

XII. The Effect of Pressure i?i Lowering the Freezing- Poi^it 
of Water experimentally demonstrated. By Professor W. 
Thomson, Glasgow^-. 

ON the 2nd of January 1849, a communication entitled 
" Theoretical Considerations on the Effect of Pressure 
in Lowering the Freezing- Point of Water, by James Thomson, 
Esq., of Glasgow," was laid before the Royal Society, and it 
has since been published in the Transactions, vol. xvi. part 5f. 
In that paper it was demonstrated that, if the fundamental 
axiom of Carnot's Theory of the Motive Power of Heat be 
admitted, it follows, as a rigorous consequence, that the tem- 
perature at which ice melts will be lowered by the application 
of pressure ; and the extent of this effect due to a given amount 
of pressure was deduced by a reasoning analogous to that of 
Carnot from Regnault's experimental determination of the 
latent heat, and the pressure of saturated aqueous vapour at 
various temperatures differing very little from the ordinary 
freezing-point of water. Reducing to Fahrenheit's scale the 
final result of the paper, we find 

^ = «x 0-0135; 

where t denotes the depression in the temperature of melting 
ice produced by the addition of w "atmospheres" (or n times 
the pressure due to 29*922 inches of mercury), to the ordinary 
pressure experienced from the atmosphere. 

In this very remarkable speculation, an entirely novel phy- 
sical phaenomenon was j)^^dicted in anticipation of any direct 
experiments on the subject ; and the actual observation of the 
phaenomenon was pointed out as a highly interesting object 
for experimental research. 

* From the Proceedings of the Royal Society of Edinburgh, February 

f It will appear also, with some slight alterations made by the author, 
in the Cambridge and Dublin Mathematical Journal, Nov. 1850. — W. T. 

124: Prol. Tlionison on the Effect of Pressure in 

To test the phoenomenon by experiment without ap))lying 
excessively f^reat pressisre, a very sensitive thermometer wouki 
lie requiretl, since for ten atmosplieres the effect expected is 
little more than the tenth part of a Fahreniicit degree; and 
the thermometer employed, if founded on the expansion of a 
liquid in a glass bulb and tube, must be protected from the 
pressure of the iicjuid, which, if acting on it, would produce a 
tleformation, or a least a compression of the glass that would 
materially affect the indications. For a thermometer of ex- 
treme sensibility, mercury does not ajipear to be a convenient 
li(juid; since, if a very fine tube be employed, there is some 
uncertainty in the indications on account of the irregularity 
of capillary action, due probably to superficial impurities, and 
observable even when the best mercury that can be prepared 
is made use of; and again, if a very large bulb be employed, 
the weight of the mercury causes a deformation which will 
produce a very marked difference in the position of the head 
of the column in the tube according to the manner in which 
the glass is supported, and may therefore affect with uncer- 
tainty the indications of the instrument. The former objec- 
tion does not apply to the use of any fluid which perfectly 
wets the glass; and the last-mentioned source of uncertainty 
will be much less for any lighter liquid than mercury, of equal 
or greater expansibility by heat. Now the coefficient of ex- 
pansion of sulphuric aether at 0° C. being, according to M. J. 
Pierre*, '00151, is eight or nine times that of mercury (which 
is '000179, according to Regnault), and its density is about 
the twentieth part of the density of mercury. Hence a ther- 
mometer of much higher sensibility may be constructed with 
aether than with mercury, without experiencing inconvenience 
from the circumstances which have been alluded to. An 
aether thermometer was accordingly constructed by Mr. 
Robert AJansell of Glasgow, for the experiment which I pro- 
posed to make. The bulb of this instrument is nearly cylin- 
drical, and is about 3^ inches long and ^ths of an inch in 
diameter. The tube has a cylindrical bore about 6,j inches 
long: about 5\ inches of the tube are divided into 220 equal 
parts. The thermometer is entirely inclosed, and hermeti- 
cally sealed in a glass tube, which is just large enough to 
admit it freely f. On comparing the indications of this instru- 

* See Dixon on Heat, p. 7~. 

I Following a suggestion made to me by Professor Forbes of Edinburgli, 
I have in subsequent experiments with this thermometer, used it with 
enough of mercury introduced into the tube in which it is hermetically 
sealed to entirely cover its bull); as I found that, without this, if the ex- 
])eriment was conducted in a warm room, the indications of the thermo- 
meter were frequently deranged by the portion of the water which was left 
free from ice becoming slightly elevated in temperature. 

Lffwering the Freezing- Point of Water. 125 

ment with those of a tliermometer of Crichton's with an ivory 
scale, which has divisions corresponding to degrees Fahren- 
heit of about Ty'yth of an inch each, I found that the range of 
the aether thermometer is about 3° Fahrenheit ; and that there 
are about 212 divisions on tlie tube corresponding to the in- 
terval of pressure from 31° to 34°, as nearly as I could discover 
from such an unsatisfactory standard of reference. This gives 
Jy of a degree for the mean value of a division. From a 
rough calibration of th.e tube which was made, I am convinced 
that the values of the divisions at no part of the tube diifer by 
more than J^th of this amount from the true mean value ; 
and, taking into account all the sources of uncertainty, I think 
it probable that each of the divisions on the tube of the aether 
thermometer corresponds to something between ~ and - j of 
a degree Fahrenheit. 

With this thermometer in its glass envelope, and with a 
strong glass cylinder (OErsted's apparatus for the compression 
of water), an experiment was made in the following manner : — 

The compression vessel was partly filled with pieces of clean 
ice and water : a glass tube about a toot long and y cjth of an 
inch internal diameter, closed at one end, was inserted with 
its open end downwards, to indicate the fluiil pressure by the 
compression of the air which it contained ; and the sether 
thermometer was let down and allowed to rest with the lower 
end of its glass envelope pressing on the bottom of the vessel. 
A lead ring was let down so as to keep free from ice the. water 
in the compression cylinder round that part of the thermo- 
meter tube where readings were expected. More ice was 
added above ; so that both above and below the clear space, 
which was only about two inches deep, the compression cy- 
linder was full of pieces of ice. Water was then poured in 
by a tube with a stopcock fitted in the neck of the vessel, till 
the vessel was full up to the piston, after which the stopcock 
was shut. 

After it was observed that the column of aether in the ther- 
mometer stood at about 67°, with reference to the divisions on 
the tube, a pressure of from 12 to 15 atmospheres was applied, 
by forcing the piston down with the screw. Immediately the 
column of aether descended very rapidly, and in a very few 
minutes it was below 61°. The pressure was then suddenly 
removed, and immediately the column in the thermometer 
began to rise rapidly. Several times pressure was again sud-" 
denly applied, and again suddenly removed, and the effects 
upon the thermometer were most marked. 

The fact that the freezing-point of water is sensibly lowered 
by a few atmospheres of pressure was thus established beyond 

1 26 Effect of Pressure in Lowering the Freezing- Poi?it of f Voter. 

all doubt. After that I attempted, in a more deliberate ex- 
periment, to determine as accurately as my means of observa- 
tion allowed me to ilo, the actual extent to which the tenipe- 
rature of freezinjT is affected by determinate applications of 

In the present communication I shall merely mention the 
results obtained, without entering at all upon the details of 
the experiment. 

I found that a pressure of, as nearly as I have been able to 
estimate it, 8-1 atmospheres produced a depression measured 
by 7,j divisions of the tube on the column of eether in the 
thermometer; and again, a pressure of 16-8 atmospheres pro- 
duced a ihermometric depression of 16| divisions. Hence 

observed lowering of temperature was —-, or "1 

former rasp, nnd 'i. nv '9^0° F in tho loffoi- 


the former case, and 

06° F. in 


, or -232° F. in the latter. 

Let us compare these results with theory. According to 
the conclusions arrived at by my brother in the paper referred 
to above, the lowering of the freezing-point of water by 8*1 
atmospheres of pressure would be 81 x -0135, or '109° F. ; 
and the lowering of the freezing-point by 16'8 atmospheres 
would be 16-8 x -0135, or -227° F. Hence we have the fol- 
lowing highly satisfactory comparison, for the two cases, be- 
tween the experiment and theory : — 

Observed pressures. 

Observed depres- 
sions of tempera- 

Depressions according to 

theory, on the hypothesis 

that the pressureswero truly 



8'1 atmospheres ... 
16-8 atmospheres ... 

•106° F. 
•232° F. 

•109° F. 
•227° F. 

-•003° F. 
-|--005° F. 

It was, I confess, with some surprise, that, after having com- 
pleted the observations under an impression that they pre- 
sented great discrepancies from the theoretical expectations, 
I found the numbers I had noted down indicated in reality an 
agreement so remarkably close, that I could not but attribute 
it in some degree to chance, when I reflected on the very rude 
manner in which the quantitative parts of the experiment 
(especially the measurement of the pressure, and the evalua- 
tion of the division of the aether thermometer) had been con- 

I hope before long to have a thermometer constructed, 
which shall be at least three times as sensitive as the aether 
thermometer 1 have used hitherto; and I expect with it to be 

Mr. J. P. Joule on a remarkable appearance of Lightning. 127 

able to perceive the effect of increasiii<r or diminishing the 
pressure by less than an alniORphere, in lowering or elevating 
the fVeezing-point of water. 

If a convenient mininmm thermometer could be constructed, 
the effects of very great pressures might easily be tested by 
hermetically sealing the thermometer in a strong glass, or in 
a metal tube, and putting it into a mixture of ice and water, 
in a strong metal vessel, in which an enormous pressure might 
be produced by the forcing-pump of a Bramah's press. 

In conclusion, it may be remarked, that the same theory 
which pointed out the remarkable effect of pressure on the 
freezing-point of^vater, now established by experiment, indi- 
cates that a corresponding effect may be expected for all 
liquids which expand in freezing ; that a reverse effect, or an 
elevation of the freezing-point by an increase of pressure, may 
be expected for all liquids which contract in freezing ; and 
that the extent of the effect to be expected may in every case 
be deduced from Regnault's observations on vapour (pro- 
vided that the freezing-point is within the temperature-limits 
of his observations), if the latent heat of a cubic foot of the 
liquid, and the alteration of its volume in freezing be known. 

XIII. On a remarkable appearance of Lightning. 
% J. P. Joule, F.R.S. 

To the Editors of the Philosophical Magazine and Journal. 

|N the 16th inst., after a very sultry morning, this town 
was, in common with a large tract of country, visited at 
4 o'clock b}' a thunder-storm accompanied with heavy rain. 
In the evening of the same day, about 9 o'clock, we had an op- 
portunity of witnessing a most magnificent display of electrical 
discharges, which continued almost uninterruptedly for the 
space of one hour, accompanied, however, by only a few drops 
of rain. I had never before seen lightning of such an extra- 
ordinary character. Each discharge appeared to emanate 
from a mass of clouds in the south-west, and travelled six or 
ten miles in the direction of the spectator, dividing into half a 
dozen or more sparks, or zigzag streams of light, in some in- 
stances the termination of each of these sparks being, as re- 
presented in the adjoining sketch, again subdivided into a 
number of smaller sparks. I did not observe any of tiie dis- 
charges to strike the ground; and from the interval of time 
between the appearance of those which crossed the zenith and 

128 Mr. J. P. Joule on a rcmarhahlc appearance of Lightning. 

the tlimuler, I consider tliat Uieir «reiieral elevation from the 
surface of the earth must have been at least .'51 miles. 

The diver<rinfj form arose no doubt from the extensive ne- 
gativesurfacepresented by the clouds, , 

and may be imitated on a small scale v. , -A^A- ^'^) 
by filling a glass jar with water and jA^ \^ i 
using it as a Leyden phial. If such 
a jar be discharged by bringing one 
ball of the dischariiiiiij rod towards 
the exterior glass surface, the other 
ball being in connexion with the 
water, the spark will, in restoring the 
electrical ec|uilibrium, diverge over 
the whole glass surface. 

Another remarkable feature in the 
lightning was the sensible time of 
its travelling towards the spectator. The main streams of 
light were always formed before the divergin.g sparks; and 
when formed, remained steady for an appreciable time, until 
the whole disappeared together. My brothers, Messrs. Ben- 
jamin and John Joule, who observed the lightning two miles 
westward of my station, formed exactly the same impression 
of its ciiaracter ; and in addition, the latter and several other 
parties were witnesses of a phaenomenon, which, if owing to 
the electrical slate of the atmosphere, was, I believe, without 
a recorded precedent. 

At half-past 8 o'clock a bright red light appeared among 
the clouds, bearing nearly due south, and having an elevation 
of about 30^ above the horizon. It appeared as if the sun 
were behind a cloud illuminating its edges strongly, and 
throwing a brilliant light upon th€ neighbouring clouds. It 
lasted about five minutes with perfect steadiness, and then 
gradually disappeared. 

I ought to mention, that, during the above-described pha2- 
nomena, violent thunder-storms were taking place in different 
parts of this county and in Cheshire, but without any apparent 
connexion with them. 

I have the honour to remain, Gentlemen, 

Yours very respectfully, 

Acton Square, Salford, Manchester, JaMES P. JoULE. 

July 19, 1850. 

[ 129 ] 

XIV. Remarks on the Weather (hiring the Quarter ending 
June 30, 1850. Ihj James Giaksheh, Esq., F.H.S., Hun. 
Sec. of the Biitish Meteorological Society, Sfc."^^ 

^T^HE weather during the past quarter has been variable, 
J- and at times very unusual. The tein{)erature of" tiie 
air till April 21 was 4^*3 above the average, and this period 
was Iree Ironi frosts. From April 22 to May 16, there was 
an average deficiency of 'y of daily temperature ; from May 1 7 
to June 9, the temperature was about its average value ; it was 
8° in excess on June II, and 13° in defect on the 15th : and 
during the follownig night the temperature of the air in many 
places was below 32°, a very unusual circumstance for the 
season. From June i 8 to the 26th, the period was warm ; the 
mean excess of temperature was 6°. Snow has fallen on 
several days during the past quarter. 

The mean temperature of the air at Greenwich for the three 
months ending May, constituting the three spring months, was 
46°'6, beini; of almost the same value as that of the average 
from the seventy-nine preceding springs. 

For the month of April was48°"5, excecding\\\^\. of the ave- 
rage of the preceding seventy-nine years by 2°'8, and exceeding 
that of the preceding nine years by 1°*0. 

For the month of May was 51°'3, being 1°*3 less than the 
average of the preceding seventy-nine years, and 3 *! /rssthan 
that of the preceding nine years. 

For the month of June was 60°*8, exceeding that of the 
average of the preceding seventy-nine years by 2°'8, andd'j:'- 
ceeding that of the preceding nine years by 1°*2. 

The mean for the (|uarter was 53°"4, exceeding that of the 
average of seventy-nine years by 1°*4, and being /es5than that 
of the preceding nine years by 0°'3. 

The mean temperature of evaporation at Greewdoich — 

For the month of April .was 45°*4 ; for May was 47°*5; 
and for June was 54^-8. These values are 1°'7 greater, 3°*0 
less, and 0°"1 greater than those of the averages of the same 
months in the preceding nine years. 

The mean temperature of the deiv-point at Greenxmch — 

For the months of April, May and June, were 41°'7, 43°"4, 
and 50°*1 respectively. These values are 1°0 greater, 4°'0 
less, and l°-8 less respectively than the averages of the same 
months in the preceding nine years. 

The mean elastic force of vapour at Greenwich for the quarter 
was 0"31S inch, being /ws than the average from the preceding 
nine years by 0"031 inch. 

* Communicated by tlie Author. 

Phil, Mag. S. 3, Vol. 37. No. 248. Aiwust 1850. K 

130 Mr. J. Glaisher's Uemar/iS on the IVeatha- 

The vican ivcight of isoatcr in a cubic foot of air for the 
(juarter was 3"6 grains. The average Iroin the preceding 
nine years was 3'S grains. 

TJte incan degree of humid ihj in April was 0'795, in May 
was 0'765, and in June was 0"702. The averages from the 
nine preceding years were O'SOS, 0'788 and 0'702 respectively. 

The mean reading of the barometer at Grcewwich in April 
was '29*59 1 inches, in May was 29' 7 14, and in June was 29'886'. 
These readings are 0"111- less^ 0*071 Icss^ and 0'0d>9 greater 
respectively than the averages oftliesame months in the pre- 
ceding nine years. 

The average "weight of a cubic foot of air for the quarter, 
under the average temperature, humidity and pressure, was 
532 grains; being of the same vahie as that of the average of 
the preceding nine years. 

The rain fallen at Greennnch in April was 2*4 inches, in 
May was 2'3, and in June was TO. The falls for these three 
months on an averageof thirty-four years, are 1*7, 2-0 and 1*7 
inches respectively. 

The avcj-age daily ranges of the readings of the theinnometer 
in air at the height of four feet above the soil, in April was 
16°*0, in May was 18" -9, and in June was 26°"0. The ave- 
rages for these three months from the preceding nine years 
were 17°'4, 18°- 9 and 19°-4 respectively. 

The minimum readi?igs of the thermometer on grass in April 
was at or below 32° on twelve nights; the lowest was 23°; 
was between 32° and 40° on fourteen nights, and exceeded 
40° on four nights ; the highest reading was 44°. In May 
the readings were at and below 32' on thirteen nights ; the 
lowest was 15°; they were between 32° and 40° on eleven 
nights; and on seven nights the readings exceeded 40°. In 
June the readings were at or below 32° on two nights; the 
lowest was 29°; they were between 32° and 40° on six nights, 
and they exceeded 40° on twenty-two nights. At Cardington, 
as observed by S. C. Whitbread, Esq., the reading of the 
thermometer on grass in April was twelve nights, in May 
was twelve nights, and in June was three nights below 32°. 

The temperature of the water of the Thames, from the ob- 
servations of Lieut. Sanders, R.N., Superintendent of the 
Dreadnought Hospital Ship, was 48°*4in April, 54°'3 in May, 
and 63°'7 in June. 

Fog was prevalent on April 6 at Dundee and Whitby ; on 
the 12th at Rugby and Whitby; on the 13th at Folkestone 
and Whitby; on the 16th at Whitby and Dundee; and on 
the 20th at Edinburgh, Berwick and Whitby. On May 8 at 
Stone and Whitby; on the 11th at Greenwich; on the 15th, 

during the Quarter ending June 30, 1850. 131 

16th and 17th, at Durham; on the 18th at Hastings; on the 
20th at Hartwell House, Hartwell Rectory, Durham and 
Whitby; on the 21st at Hartwell House, Hartwell Rectory, 
Berwick, Whitby and Durham; on the 22nd at Brighton, 
Darlington, Durham, Dundee, Berwick and W^hitby ; on the 
23rd at Darlington, Durham, Dundee and Edinburgh ; on 
the 24th at Hartwell House, Darlington, Yarmouth and 
Whitby ; on the 25th at Whitby ; and on the 3 1st at Berwick 
and Hartlepool. On June 1 at Berwick, Sunderland and 
Dundee; on the 2nd at Berwick; on the 3rd and 4th at 
Edinburgh; on the 5th at Folkestone; on the 17th at Sun- 
derland ; on the 18th at Glasgow ; and on the 20th at White- 

Meteors. — At Stone, on April 10, at 10^ p.m., a meteor shot 
from Jupiter to y Leonis. On May 2, at lO'^ p.m., a meteor 
shot from Virgo about Ap from Jupiter, and went as far as 
Jupiter; on May 29, at 10^ 5^ p.m., a meteor shot from 
« Cygni southwards. On June 4, at ll'^^ 28'^ p.m., a meteor 
shot from a Urs. Min. (Polaris) to S Urs. Maj.; on the 
16th, at 0^ 25°^ a.m., a meteor shot from the west of /3 Cas- 
siopeje and went 4° north ; on the same night, at 0^^ 40"^ a.m., 
a splendid meteor, larger than a star of the first magnitude, 
shot from the west of Capella 10° east of due north, and about 
15° above the horizon, and went in a westward direction near 
to the star 31 Lyncis, leaving a train of blue light of about 
20°; a few seconds after a small meteor shot from above Po- 
laris to Cassiopea ; on the same night, at 0^ 45°^ a.m., a 
meteor shot from /3 Serpentis, and went about 5° south ; at 
1^ 3™ A.M., a meteor shot from s Bootis to Arcturus ; at 
li» 20"^ A.M., a meteor as large as a star of the first magnitude, 
and of a beautiful red colour, shot from s Urs. Maj. and passed 
by a Urs. Maj. On the 20th, at 1 1'^ 42"^ p.m., a meteor shot 
from a Lyrae to « Cygni ; on the 24th, at 1 1^ 30™ p.m., a me- 
teor as large as a star of the first magnitude shot from Arcturus 
and went 20'^ magnetic west', leaving a train of blue light. 

On June 4, at Hartwell Rectory, a small meteor was seen 
from Polaris to the Pointers, at 1 1'^ 30™; on the 21st a me- 
teor shot from a Lyrae to u Cygni at 1 1'* 42™ p.m.* On June 24 
a meteor was seen from Arcturus to within 10° of the horizon 
at 11*1 30«>. 

At Nottingham, on May I, at 10^^ 33™, a meteor of the size 
of a star of the second mag. fell slowly from 30^ above S. 
horizon, at an angle of 40° to west; anil at 11^^ 10™ another 
fell downwards 5° south of Jupiter. May 30, at 10^ 38™, a 

* This is evidently the same meteor as that observed at Stone, but which 
is referred to June 20 : which day is right ? 


1:5'J Mr. J. (iluislier's licmarhs on the Weather 

meteor, size second mag., colour yellow, passed nearly liori- 
zonlally 1,'° under Ve<>a, niovino; to south. June 1, globe 
meteor, size of Jupiter but less bright, of a red colour, luiving 
a well-defuied {lisc, moved tVoin y through f Cassiopeaa, ended 
S*^ cast ola I'ersei, duration 1,} minute. On the.'ird, another 
size, third mag., blue colour, ill-defined, passed from a Cygni 
through Lacerta at 10'' 30"'; and at lO'' 45'" a nearjysiniilar 
one from X Draconis through >j Draconis. 

Solar Halos were seen on April 1 at Greenwich ; on the 
2nd at Stone and Ilariwell Rectory; on the Ttli at Greenwich 
and Stone ; on the 14th at Stone; on the 17th at Nottingham; 
on the 18th at Guernsey, Greenwich and Nottingham; on 
the 19lh at Stone and Nottingham; on the 21st at Hartwell 
Rectory; and on the 25th at Greenwich and Nottingham. 
On May 4 at Durham ; on May 5 at Uckfield ; on May 7 at 
Durham; on May 13 at Uckfield; on May 14 at Hartwell 
Rectory; on May 19 at Durham; on May 23 and 26 at 
Hartwell Rectory; and on May 28 at Nottingham. On 
June 2 at Nottingham and Whitehaven ; on the 3rd at Not- 
tingham ; on the 4th at Greenwich, Stone, Hartwell Rectory, 
Nottingham, Stonyhurst and Durham; on the 5th at Stone; 
on the 8th at Hartwell House; on the 9th at Stone, Rose 
Hill, Oxford, and Nottingham; on the lOth at Southampton, 
Stone, Hartwell House, Cardington, Rose Hill, Oxford, 
Norwich and Nottingham ; on the 11th at Stone, Rose Hill, 
Oxford and Nottingham; on the 12th at Nottingham; on 
the 14th at Cardington ; on the 16th at Stone, Rose Hill, 
Oxford and Nottingham; on the 17th at Stone and Ayles- 
bury; on the ISth at Aylesbury; on the 20lh at Stone and 
Nottingham; on the 21st at Stone and Nottingham; and on 
the 29th at Uckfield and Nottingham. 

Liinar Halos were seen on April [6 and 17 at Hartwell 
Rectory; on the 19th at Wakefield; on the 20th at Liver- 
pool; on the 21st, 22nd, 23rd, at Hartwell Rectory; on the 
24th at Stonyhurst. On May 20 and 22 at Uckfield ; and 
on the 26th at Stone. On June 16 at Stone and Haitwell 
Rectory; on the 18th at Stone; on the 20th at Guernsey, 
Stone, Hartwell Rectory, and Radcliff'e Observatory, Oxford; 
on the 21st at Jersey, Stone and Hartwell Rectory; and on 
the 25th at Uckfield. 

Fara&elencE were seen on May 28 at Durham; and on 
June 20 and 21 at Stone and Hartwell Rectory. 

Perihelion was seen on May 21 at Nottingham. 

Aiirorce burcalcs were seen on A))ril 5 at Whitehaven ; on 
April 6 at Durham ; on May 12 at Aylesbury, Oxford, Stony- 
hurst and Durham; on June 5 at Highfiekl House, Netting- 

during the Qimrlcr ejidiiig June 30, 1850. 133 

ham ; on June 13 at Hartwell House, Radcliffe Observatory, 
Oxford, and at Rose Hill near Oxford ; on June 26 near Man- 
chester; and on June 27 at Noltiugham and at Chesterfield. 

Thundcr-stonns occurred on April 2 at Wakefield, Leeds, 
Liverpool, Stonyliurst and Whitehaven ; on the 8th at Uck- 
field ; on the 10th at Aylesbury; on the llth at Hartwell 
Rectory, Stone, Cardington and Saflron Walden ; on the 
12lh at Uckfield, Greenwich, London and Saffron Walden ; 
on the 13th at Greenwich; on the 17th at Norwich ; on the 
20th at Holkham, Nottingham and Exeter ; on the 23rd at 
Hawarden. On May 7 at Uckfield; on the 13th at Leeds 
and Hawarden ; on the 17th at Uckfield; on the 19th at 
Derby; on the 22nd at Stonyhurst; on the 23rd at Stone, 
Hartwell Rectory, Hartwell House, Leinslade, Bucks, Rose 
Hill, Oxford, Cardinoton, SafTron Walden, Derby, Notting- 
ham, Liverpool, Leeds and Manchester; on the 24;ih at Hart- 
well Rectory, Stone, Hariwell House, Rose Hill, Oxford, and 
Radcliffe Observatory, Oxford ; on the 26th at Norwich ; on 
the 27th at Leeds, Manchester, Durham and North Shields; 
on the 30th at FLartwell House, Liverpool and Stonyhurst; 
on the 31st at Slone and Rose Hill, Oxford. On June 5 at 
W^akefield, North Shields and Durham ; on the 6th at Hart- 
well House, Hartwell Rectory, Leeds, Stonyhurst, Durham 
and W' hitehaven ; on the 7th at Leeds; on the 12th at Hel- 
ston ; on the 13th at Uckfield; on the 16th at Durham; on 
the 17th at North Shields; on the 25th at W^akefield and 
Leeds; on the 26th at Guernsey, Helston, Falmouth, Truro, 
Exeter, Uckfield, Southampton, St. John's Wood, Greenwich, 
Stone, Aylesbury, Hartwell House, Hartwell Rectory, Lein- 
slade, Bucks, Saffron Walden, Radcliffe Observatory, Oxford, 
and Cardington; on the 27th at Guernsey, Jersey, Exeter, Chi- 
chester, Uckfield, Helston, Southampton, St. John's Wood, 
and Hartwell Rectory; on tlie 28tii at Greenwich, Chichester, 
St. John's Wood, Uckfield and Hartwell House. 

Of these storms that of the 26th of June was the worst. It 
was described by J. Johnson, Esq., of Oxford Observatory, as 
the most violent storm of thunder and lightning ever remem- 
bered there. It began about 2^ 30™ p.m., and lasted till about 
4,h 3Qra pj^j^ Two college towers were struck by lightning. 
No life was lost; but he had heard of five persons (three 
children) who were thrown down by the violence of the light- 
ning. There appears to have been two storms, one succeed- 
ing the other after an interval of about thirty minutes. I 
was not here myself, but the storm lias been described to me 
by two trustworthy persons as terrific. As far as I can make 
out, the storm passed over the town in a N.N.E. direction. 

At Hartwell Rectory, the Rev. C. Lowndes states, "that on 

ISi Mr. .). Glaisher's Remarks on the Weather 

the 26tli thunder was heard at l'» 30™ p.m., and at 3 p.m. 
tlierc was a heavy storm with thunder and Hr^htning : it con- 
tinued stormy during the evening and night." 

At Hartweil House, Mr. Horton says, "that on June 26 a 
mansion near Thame, called Thame House, about ten miles 
from here, was set on fire by the lightning." 

At Truro, Dr. C. Barham says, " the thunder-storm on 
June 26 was rather severe, but more so a few miles to the 
northward. Eleven sheep were killed by the lightning in one 
field, and four in a neighbouring one about ten miles to the 
north-east. The I'ain was not very heavy, and there was no 
hail: there was a fall of 16^ of temperature between I'^and 5*^ 
P.M., and the weather has continued unsettled with showers 
and squally from that time to the present, July 3." 

At Exeter, Dr. Shapter remarks, "that for three days pre- 
viously to June 26 the atmosphere had gradually become hot 
and sultry, and at 4 p.m. on this day it became extremely op- 
pressive. Distant thunder was then heard, and heavy rain- 
clouds came up with a light wind from the south. At 6 p.m. 
the storm reached Exeter; the lightning was constant and 
vivid, and heavy rain fell for two hours, when the storm mo- 
derated and passed on, and the wind shifted rather suddenly 
till 6 P.M. It reached Bridgewater at about 9 p.m. The elec- 
tric telegraph on the South Devon Railway was rendered 
useless for several hours; the trains were consequently de- 
layed, and considerable inconvenience was occasioned. The 
general character of the other parts of the month was fine and 
warm. Rain to the depth of 1-21 inch fell during the storm." 

At Uckfield, C. L. Prince, Esq. says, "that on the 26th, at 
night, the electric fluid struck a house in this place and shat- 
tered a portion of the roof, burnt some clothes, &c., and in- 
jured no one, although there were thirty persons under the 
roof at the time." 

At Southampton rain to the depth of r96 inch fell during 
the passage of the storm. 

Thunder was heard, but lightning was not seen, on April 11 
at Rose Hill, Oxford, and Saffron Walden ; on the 1 2th at 
Saffron Walden and Norwich ; on the 17th at Hartweil 
House; on the 20th and 21st at Nottingham. On May 7 at 
Guernsey; on the 13th at Cardington, Stone and Aylesbury; 
on the 17th at Nottingham; on the 18th at Wakefield and 
Nottingham; on the 19th at Cardington and Nottingham; on 
the 21st at Exeter and Ha warden ; on the 22nd at Aylesbury 
and Holkham ; on the 23rd at Aylesbury, Norwich, Holkham, 
Oxford, Wakefield and Stonyhurst ; on the 24-th at Carding- 
ton and Hawarden ; on the 25th and 26th at Hawarden ; on 
the 27th at Guernsey, Wakefield and Stonyhurst; and on 

duri7ig the Quarter ending June 30, 1850. 135 

the 31st at Hartwell Rectory, Leinslade, Bucks, Cardington, 
Oxford, Liverpool, Stonyliurst and Whitehaven. On June 5 
at Nottingham and Dundee ; on June 6 at Stone and Nottini;- 
ham ; on June 7 at Nottingham ; on June 9 and 11 at Stone; 
on June 12 at Helston ; on June 16 at Stony hurst ; on June 25 
at Nottingham ; on June 26 at Jersey, St. John's Wood, 
Waivefield and Nottingham ; on the 27th at Stonyhurst ; and 
on the 28th at Jersey. 

Lig/ifnhig was seen, but thunder was not heard, on April 2 
at Stone and Stonyhurst; and on the 20th at Nottingham. 
On May 2 at Stone; on the Sth at Guernsey; and on the 
30th at St. John^i Wood. On June 5 at Nottingham ; on 
the 24th at Nottingham ; on tiie 25th at Cardington and Not- 
tingham ; on the 26th at St. John's Wood ; on the 27th at 
St. John's Wood and Aylesbury; on the 28th at Aylesbury 
and Cardington ; on the 29th at Aylesbury. 

Hail fell on i^pril 3 at Liverpool ; on the 4th at Stone and 
Liverpool; on tlie 15th at Liverpool; on the 17th at Not- 
tingham ; on the 20th at Truro, Exeter, Saffron Walden, 
Cardington, Holkham, Norwich; on the 21st and 22nd at 
Nottingham ; on the 25th at Rose Hill, Oxford ; and on the 
30rii at Guernsey. On May 1 at Holkham and Saffron 
Walden ; on the 4th at Leinslade, Bucks, Saffron Walden 
and Cardington ; on the 5th at Oxford, Wakefield, Durham 
and North Shields ; on the 6th at Guernsey, North Shields 
and Durham; on the 9th at Uckfield ; on the 14th at Rose 
Hill, Oxford, and Durham ; on the 15th at Greenwich, Ayles- 
bury, Stone, Hartwell House, Leinslade, Bucks, Cardington, 
Radcliffe Observatory, Oxford, Saffron W^alden, Stonyhurst, 
W^hitehaven, Durham and North Shields; on the 17th at 
Uckfield ; on the 23rd at Stone, Cardington and Nottingham ; 
on the 31st at Hartwell Rectory. On June 6 at Nottingham 
and Stonyhurst; on the 10th at Uckfield, Hartwell House 
and Yarmouth ; on the 16th at Durham ; on the 17th at Uck- 
field; on the 19th at Aylesbury; on the 26lh at Helston, 
Stone, and Rose Hill, Oxford ; on June 27 at Uckfield. 

Sno'du fell at Aylesbury on April 29; at North Shields, 
Whitehaven, Beattock and Edinburgh, on May 5 ; at Leeds 
on May 8 ; at Wakefield on May 9 ; at North Shields on 
May 15; at London on the 16th ; and at Stone on the 23rd. 
These falls of snow in May are very unusual. 

T/ie /wrizontal movement of the air at Green'wich in April 
was 110 miles, in May ^Q miles, and in June was 90 miles daily. 

The series of observations of the direction of the loind, 
taken at the various railway stations, and published by the 
Daily News, has continued wiih great regularity ; and the 
following Tables have principally been formed from them : — 


_=3 aj 


"S ^ 



"3 .£ 

th of Birmingham. 


in many places. 

h of Whitbv. 



E ^* 

^ a> 
c3 > 

o a) 











= ^^ 

_ . 


.3 ca 



> 2 

ain Sou 

1 every> 

Rain i 

ce Nort 


2 o 

ces. Fi 

at Shap 



^ o 

"" o 

in strength. 

of wind and r; 

and hard wiiu 

to the South. 


e at every pla 

e at most plac 
and rain to tl: 
!c breeze. 

most places, 
ud rain at mos 
e at many i)la 

e at most plac 
otion. Rain to 
e at most place 

e at many pla 
n strength, 
day. Frosty ; 
lotion. Rain 

e at a few pla 
e to the Soutl 



«j - 

ntle n 

S a; ■= 

most ] 
id at 1 
,ind a 

g S g 

aj u o 

iable i 
ntle n 

S3 N C 

a; aj _o 



— to 

:§ = 

t) .3 

Wind va 
Heavy st 
Strong 1) 
Strong b 
Air in ge 
A strong 

A gentle 
Gentle b 
Calm an( 
Calm at 
Hard wii 
A hard v 
A strong 
A gentle 
A strong 

A strong 
Very vari 
Nearly a 
Air in ge 

A strong 
A strong 
Air in ge 
Wind vai 

„ C « 

6 6 

.• o -i o c3 c3 



&■ o d 

ci <u d 

^ ^ ^ 


U u V 

53 Js'S 


. & n 

"^ .2 oJ 


o a5 ej .2 

c>i !2 "2 

. 3 ca 

c 1 1 '^ ^ 2 1 

'S '^ «i «j S 'S 


> »3 

" > ^> > > 



'$. > > 

> > to 

to > > 


„t; m 

is " a3 



<u ^ 

d d 

d d 

2 C.2 


oj c; 



a & 



3 5 


to en «> 


> > 

> > 

a n 

& " e: > 

Qj aj 

a3 aj aJ 

^ d 

O t- CJ 

K* r* 


aj • 

m .. "5 

"ca , . "S ^ 

•; . t:' 

? ? c3 ca 

d q3 d 


= g 1 


" c>J-r: 

■r: =*i -r; ^ 

i, '" Ji 



. rt 

rt . ca 


« u 

lA M ~ tK 

al > 

t- to > 








5 ^ 'S 

to ""^ 


^» 2 

s ^ t^ &: 

1^ S: 

^^ aJ aJ 

: d <id 




c-2 o 


XI CD ~ ai .to 

to r 

3 " 

~ 3 - 

■ ^ 










o ^ <u . 



aJ a5 


—t'^ . aj 


ca > . tn 

=j c3 "^[i 

to *L. *;^ 

fi-;! d ^ 

aJ q3 d 






ca ca 




> s '" 



> > 





aj a3 is a3 

O 3J 

is cJ 

d d 

d d 

t) rj . 



,/ -r- -r oo . ,/ 
S 5 . <4 

"1 ^ 

^5 *i to ^ 

& 3 

c3 - ca 





>• > 1; -^ 

to "* 

> > 

s > 



c^ ^: N « t^ t^ 

^ " ^ 

^ aJ «:' ^ 

^ ^ >• 


_; aj ^ 



"*^ '^ « 

•■ H ^" ^! a3 fi 

^ "^ CO 

aj QJ . ^ 

&; i i 

j: ^ & d 

d d a3 


to to 

to to to 

S <o to 

~ C S M 

" ~ " 



ij _d is ^ ii 

_o o 

^ aJ 


5 i ° 


1^ " 

.2 * .2 ^ 


^ d s ^: 

aj d d 




ca . « c3 

t» to 

3 5 


^- ^ 

r-iOJrO'Si>f5i£C0020i-<NCOi.'5 0l>.CCClO 

M C^ '^ 1.-5 

•-3 1^ 05 1 


rt ^ « 

rt >-l rt l-H 

r-- rt ca 

CJ '.^1 pa <M 

ca CJ 


« ^ ^ IS = > ^ ' 


, Cal 


.S§ J,^-55 2J 


5. H 




.Eg'-" ^^^ S6 

•^ --» c3 ,.; — >-i . (u •-! 

V u Sv: '^\1 >. «o 

:§^ri§ ^£« 5 .sz 

le at 
; mos 

t She 


1 the 

some places, 

•gh. Snow at 
h. Heavy ga 
rong breeze at 
ces. Calm an( 
lie North. 

places. Rain t 
(laces. Snow a 
places. Hard 

'ccasional rain 
aces. Fog at 

og to the Nori 
og to the Nor* 
;he North. St 
aces. Rain ii 


try at Crewe. 



e motion, 
e motion, 
ze. Calm in 
eeze in some 
rs at Edinbhi 
il ill the Sout 
to the S. A st 
le. at most pla 
[jcze at most 
and rain to tl 
ze and calm, 
e motion, 
eeze at most 
»cze at most ) 
eeze at most 
liii day. 
st places. 
ze at most pi 
ze and calm, 
lin day. 
st places. F( 
st places. Fi 
eavy rain to 1 
ze at most pi 
eeze at most 
e motion, 
ze at most pi 
lin day. Sul 




it m 


ly e 
.t m 
it m 


ly c 

ir in 
ir in 

'toil! S 

ain g 
ard V 
ir in 
aim a 
alin a 
aim fi 
aim a 
ir in 


C r 

d 6 osidd^-S ?uc33 c3o (u <u o 





















^ S S 

*:c3"''"- 3333r;^ ?353 33 3?3 ca 


o"? S 

^ ojv ^oajsjcj c5 c3 

•1 i-^ 


w. & 




, Sr ,s. 






w. & 














" " 

£ > A ^> > > > > > 

e K 

~ ^ ajo^^g; d ^ i ^ '^ '" B 



w. & 
w. & 


. & n 



& n 
w. & 





, &s. 
,w. & 

,w. & 


= 23 

" '-' 

~ J >SajS^ ^ >i»to!oto> 




"^'i,;^ i«j«i«-:c5^>'^^"-'?^ :'^^=i»s;^M^»»; : 

cl " 




cJMc3 .. 6 _■ 6 6 6 d. 








n. & e 

1. & e 





S5 O 




>oo. S» > - >■ > > > 


Iddisddd d d d dd&>d 

■ V 



w. & 










. & 11 
w. & 

, &s. 



\ > > £ > > > > > > C>^o5> 

c 2 5 


On the 



• : ^* ^" 5= ;! d « X « «• ^ '^ = N ^ ^ ^ =<; ^ ^ ^' ^ ^ ^- ^ '''• 


.^•^.... ..• .=="^ ^ ".d. 

5 S S 

>. o 


S 2 


^ 5 J 

— ~ c 


^Z *^ . ^ 5 -I •£ 

■" ■" S 3 2 o o 

g 25^2- £ £ : 
■^ tc to ^ = 5 rt "? ■■ 

- o 

.s ^ 

- S 

~ " ~ • 

c «i =J= 

rt — . o t: 


= s <u;^ 


'5 t^ " 



al to 
to tl 



^§ = 



en -u SJ > 

<U t3 to " 




-o«:= fr:u 

c c 

rt S 

s S M ^ M o 5 3 

— oscs3'ca;3i-h 

j; = o 

« Is « '-3 - 

o — o o 

)^ a a a a 

a S3 to H a 

£ a 

<i> ^ o 
— o 

2 o - vj 

"w a.' ~ 

' - •5 = — ■.-" s c rt' s 

1 tb => fco ^%^ tr, to _ to to „ 

T ^ T *^ - T T "^ T T =^ ' 

— C O . o -« 

So g ^ o _c 

"3 S ~ O) 

— — ^ "-1 

„, P S-a en 3 C-g 

3-5 — _ tD'S X* to S 

— to a " !- "^ 

to J: o !- to a •_ .s 


3 5= is 

«. S: «> ^ . 

. <*j oa «a M 2 


o o 

"5 3 rt 


^ ^ 


CA a 

> > 

en .2 - 
is ra aj 

2 a .S 
§ <u 55 

c 3 3 

O SJ U o . 

t- i- 1- ^* , 

cs cd cd . u 

> !» > a> 

aj «3 c5 ^ 

^ "5 "5 "rt jj 
OT 'S 'H 'C ^ 

rt 3 « ^- 

a ^ .2 ^ ^ .2 ? ^ .2 a ^ ^ ^' .2 


C3 « 


:•£ o 

oj ^ <u s3 ,^ 

M i3 n rt "'J 

^■^ ^ 


n rt 

a 'S a ■ 

2 * 

'^ CO 

rt ■« . 
tS C3 CO 

'>5 S • "^■^ 

i & ? ^ 

i =<j i<J c<j 

; «« « tn" 

^ .2 C a 

^ :^ s= 

^ >• 

> & <^ £: ^ 

^. ,A iS- ^ oi '^. H 6 ^ 
acooaa — 

O O 1) i) 

" .X o .2 

S'=y'=^-SaS = '^- 
. . cs & ^ & 
^ ^ > "^ ^ 

? (U^^_2^ ;f^ a ^ 

" ^ .3 ._ 

5 3 

6 <u A ^ 


Mr. J. Glaisher's Itemarks on the Weather. 1 39 

The mean monthly values of the several subjects of investi- 
gation din-ing the past (juarter are jniblished in the Quarterly 
Report of the Registrar-General. Their quarterly values are 
shown in the followiufj table : — 

ihe mean of the numbers in the first column is 29*561 
inches, and it represents that portion of the reading of the 
barometer due to the pressure of air; the remaining portion, 
or that due to tiie jiressure of water, is 0"322 inch; the sum 
of those two numbers is 29'883 inches, and it represents the 
mean reading of the barometer for the quarter ending June 30, 

The mean of the numbers in the second column for Guern- 
sey, and those places situated in the counties of Cornwall and 
Devonshire, is 53^*5 ; at Liverpool and Whitehaven is 51°'6; 
for those places situated south of latitude of 52° is 53° ; for 
those places situated between the latitudes of 52° and 53° is 
52°; between latitudes 53° and 54° is 51°-0; and for Durham, 
North Shields and Newcastle is 49°*3. The fall of rain was 
greatest in Cornwall and Devonshire, averaging 8*3 inches; 
and it was the least between the latitudes of 52° and 53°, ave- 
raging 4°'8 inches. 

The highest leading of the thermomete)' iti air was 87° at 
Uckfield and Nottingham ; and the lowest readings were 25° 
at Uckfield and 26° at Wakefiekl. The extreme rani;e of 
temperature during the quarter in England was therefore 
about 60°. 

The least daily ranges oftemperatiire took place at Guernsey, 
Liverpool and North Shields; their mean value was 10°*4: 
and the greatest occurred at Uckfield, Aylesbury and Hart- 
well ; their mean value was 21°-3. 

The least monthly ranges of temperature occurred at Guern- 
sey, Torquay and Liverpool; their mean value vyas 25°'l. 
The greatest took place at Uckfield, Aylesbury and Notting- 
ham, and their mean valu^ was 45 '8. 

Rain fell on the least number of days at Flelston, Holkham, 
Norwich and Newcastle; the average number at these places 
was 33. It fell on the greatest number of days at North 
Shields, Wakefield and Derby. The average number at these 
places was 56. The places at which the largest falls took place 
were Southampton, Stonyhurst and Exeter ; and the average 
amount at these places was 9*5 inches. The smallest falls . 
occurred at Harlwell, Holkham and Liverpool ; and their 
average was 4 inches. 

Wheat in ear, on June 9 at Aylesbury; on the 10th at 
Leinslade anti Hawarden ; on the 11th at Holkham; on the 
12th at Cardington ; on the IGth at Helston, Stone, Hartwell 

-L i 

-^ rS 

z '-> ^ 

— /I 

— ncs o 2 « ar^o » -» s a s 75 o o = m an -» a r>.«i « — o = o s 


iHs :555 r^^MUvM :5iil5i§SSl5Sllssl3 


-OOTl 1 

[»jrn^ 1 

i?2 ^'svv ss:;^?^^?::; :\;t^zzztt^'::i%%^^z^z 


JO 3Mi.)p m3|f 

b i • i b b b i b b i i i b i i tt'bt '^'^bbhi'b^'i^'ilb b b 


K .- . . ■ •; 

lOo; JW{n!> < ot jnnd 
-«.i JO iqiUp.ti 'tnK»n 

^i: ::f ? m:s::!::s:: :-;2SS2SbS2?2bbnbf ; 


i;^:^S? ^?^-S?SS?rS :^5-;'^'?/«'^^a::St?.ri."bIS 


-J03 junouv 

cr^aia)aci'>.3tt>.xb«)'>i<3ia^«i^nn'<b '^isTi^isoiCT'iijo. T'-i^' ;« 


•Airp jo i^jtmix 

3 5;??. 3 :S555?5?5V'5V5S^SSS«'?S??S'S',-3;'SI?S 


jo jaiumn ttoif 

S2S :|^ : :| :|^ :^ :?!? :-l^^^S^ -Itl?:??: : -t ^1 





^ 1 -93.:ip [ciatuo 

= 2 :^ ==22 .: -2 :: 5= = = = .•-.-'..: . 22 : » -2 =3 




W^'^UUU • • b • ' -^ ' b b i* b • CT CT ^ ' — b ' - Ti - i- ^ ^ • — b * " 

•juifKl-.visp aqj 
JO 3Jn)ci.>iIti») a«»ji( 

41 :«S ^Sliilllili :SSIJ|S¥ls«SSi?lil 


i3jnjius<Jtjj;»j jf> s^cTBu 

'l5l551liii|SE|llii :S|;iS5l :SIIs:i|S|t 


■sdiroi .(itpnom uesj^ 

•liUKSiiiiiiiiii J :iiiise :is«isiisj 


JO s^upj iitcp unsij 

^iiiiiiil m:imM :iiiiiS ^illSiiiiEi 


aqj JO ilutpntsu jsojiiyi 

'iiiiiiiisijiiiiiiii ^iiiiii -mmMm 


JO Haipvii juan^iH 

.5ii!|||||i2«l||l| :ii||S| :R«!SR!I|£ 


•JIB 9ttJ 

JO ajm«i»du3»j n^ajf 

s, n s — -c X x -X .<-. .o r , s -.s ci s-.-c =■. c. = .-. ■■; ■M r-. -r sr.-o — o. T-. ■-, -c -r -, — -c - 

b. CT 

•»« sqi JO 
pA^l atjj oj paonpai 
jtn JO 3jn»s3i(l treaj( 

ili ^ '■ '-l '-limi'llll ^mill ^lllttllii ;i 



:;:::::::-:•:■.•.;:: :t; ::;::: : • 


■ 5 


5 - 


Mr. J. Glaislier's Remarks on the Weather. \\\ 

House, Hartwell Rectory and Oxford; on the 20th at Not- 
tiniiham; and on the 24-th at Leeds. 

Wheat injUrj:cr. on June 8 at Jersey ; on the 10th at Uck- 
field ; at Guernsey on the 1.5ih; at Ilolkham and Stonyhurst 
on the 20th ; at Stone on the 21st ; at Ilawarden on the 22nd ; 
the white at Wakefield on the 22nd ; the red, in the same 
field, on the 26th; on the 23rd at Helston, Hartwell, Lein- 
slade and Derby; the 2ith at Hartwell Rectory; the 25th at 
Cardington ; the 2Gth at Nottin_frha:n : on the 28th at Rose 
Hill near Oxford ; and on the 30th at Leeds. 

Hai) begun to be gathered, at Hartwell Rectory and Stone on 
the 18th of Jnne; on die 24:lh at Hawarden and Whitehaven; 
and on the 27th at Durham. 

The common lilac in Jlo-ji-er, on April 22 at Jersey ; on 
April 25 at Guernsey; at Helston on April 27; at Uckfield 
on May 5; on the 10th at Hartwell House and Wakefield ; 
on the lith at Aylesbury ; on the 12th at Hartwell Rectory, 
Raik'liffe Observatory, Oxford ; on the 13th at Rose Hill 
near Oxford; at Stone on the 16th; at Hawarden on the 
16lh; on the 19th at Nottinghani; on the 20th at Carding- 
ton ; on the 22nd at Leeds; on the 23rd at Derby and Holk- 
hani ; on the 27th at Stonyhurst ; and on the 30th at Durham. 

Ihe cuckoo was first heard, on April 1 1 at Uckfield ; on 
the 12th at Stone; on the 16th at Whitehaven: and on the 
21st at Hartwell. 

The nightingale was first heard, on April 7 at Uckfield ; 
at Hartwell Rectory on the 12th; and at Stone on the IGth. 

The first sxi-alloio seen, on April 3 at Stone; on the Ibth at 
Whitehaven; on the 22nd at Hartwell Rectory; and ^L^y 21 
at Durham. 

At Rose Hill, Oxford, as observed by the Rev. John 
Slatter, F.R.A.S., the swallows on May 6 were packed 
together in a mass under the lee of a chimney, after flying 
about in vain tor food, and even searching for flies by creeping 
amongst the weeds in a garden, and turning up the leaves as 

General remarks and agricultural reports. — At Exeter April 
was an unusually wet month, the amount of rain being more 
than double the average for April here. I'he mean tempera- 
ture however was about 3" above the average. 

The general character of May, as compared with those of 
former years, was rather cold and wet. The amount of rain " 
was about A an inch above, and the temperature was about 2^ 
below the average. 

The mean temperature and the total amount of rain during 
June corresponded very nearly with the average of the pre- 
ceding twenty years. 

142 Mr. J. Glaishei''s Remarks on the Weather 

Aylesbury. J. Dell, Esq., F.Il.A.S. 

From the snuill (juanlity of rain that has fallen during the 
last six months, umicIi inconvenience is bcginnino- to he felt 
n-om the short supply of water. The large reservoir, which 
usually contains a suflicient quantity of water to supply the 
county jail tluring the summer months, has now only 5 feet 
in tiepth, although the usual allowance has been considerably 

Agricultural report for the quarter ending June 30, 1850 : — 

Uck field. From C. L. Prince, Esq. 

During the first three weeks the weather was for the most 
part stormy, with a considerable fall of rain; but the tempe- 
rature was more equable than is usual al this season of the 
year, there being a total absence of frost during this period. 
March having l)een unusually dry and favourable for agri- 
cultural labour, the heavy rains of April have been very 
beneficial to the grain crops. There were slight frosts on 
several morninijs durino; the last week, but not severe enouah 
materially to uijure the progress of vegetation. After the 
first week in May the weather was seasonable ; the warm 
growing showers which fell at intervals hastened vegetation 
considerabKs and proved very beneficial to all the crops 
situated on the dry soils in this neighbourhootl. A severe 
frost occurred on the 3rd of May, which in many situations 
almost entirely destroyed the forward blossom of the cherry, 
pear, plum, gooseberry, &c. Ice was observed an eighth of 
an inch in thickness, and the reading of a self-registering 
thermometer placed on grass was 21°. The temperature 
during the first three weeks of June was very variable, antl 
the thermometer in the shade ranged from 32° to 84° ; the 
extreme range of the month however was 70", viz. 30"^ in the 
morning of the 16th, and 100° in the sun on the 26th. The 
low temperature just noticed is vgry unusual for the season ; 
and had not the fruit been protected by the foliage, it must 
have been very much injured. Ice was observed early in the 
morninn;, and there was a hoar-frost on fjood radiating sur- 

Stone. The Rev. J. B. Reade, F.R.S., says, "The effect 
of the frost on June 16 on the clay land in the Vale of Ayles- 
bury was severely felt. The potatoes were greatly injured, 
and in some places the kidney beans were completely de- 

Hartvvell House. Dr. Lee says, "that on June 16 the po- 
tatoe tops were much frozen." 

Hartwell Rectory. The Rev. C. Lowndes, F.R.A.S. 

On the night of June 15 the frost was so severe as to damage 
the potatoe crops very severely on the low grounds. 

during the Quarter ending June 30, 1850. 143 

Nottingham. E. G. Lowe, Esq., F. R.A.S. 

The following are tl>e present appearances of the crops in 
this neighbourhood : — Wheat fully an average, and looks very 

Oats and barley will be a poor crop on hot sandy land, and 
very short in the straw. On cold clay lands it is likely to 
be good. On the whole they will be both below an average, 
as the dry hot weather in .Tune, which was very favourable to 
wheat, was quite the reverse to oats and barley. 

The hay crop will be much below an average. Much has 
been cut, but the recent rain has prevented half of this from 
being as yet housed. 

Beans and peas are but little grown about here; but where 
they can grow, they are spoken favourably of. 

Turnips and mangelwurzel are good in some localities and 
bad in others. 

Clover has not been an average. 

Amongst fruit, currants and gooseberries are exceedingly 
abundant, especially the latter ; and there are plenty of straw- 
berries. Apples, pears and plums will be very deficient, 
although in some places the latter are abundant. Apricots, 
peaches and nectarines are very deficient, though the former 
has turned out the best crop of the three. 

Hawarden near Chester. From Dr. MofFatt. 

From early in March to the beginning of June, oats, barley, 
potatoes, turnips, &c. were put into the ground in their season; 
the seed time was a very favourable one, and the land was in 
good condition for its cultivation. From the extreme cold 
which prevailed at the end of March and beginning of April, 
and the want of rain from the middle of April to the second 
week in May, grass was scanty, and cattle were not turned 
out so early as usual ; but the rains of the end of May and 
beginning of June were just in time to retrieve the coming- 
crop from its wavering condition. 

Potatoes have been planted to a greater extent in this than 
in former years; and if we may judge of their condition from 
the appearance ot the stalk, &c., they are healthy. There 
are rumours however of " the tlisease." I find that everybody 
has heart! of a reappearance of the disease, but it has not been 
seen by any one in this immediate locality. 

Turnips look well, and I have not heard of the usual com- 
plaints of "fly" and " worm." Disease has been very com- 
mon among cattle since the end of last March, and many 
farmers have had serious losses; indeed, one informed me, 
the other day, that since the 16th of that month he had lost 
ten cows from disease of the lungs. 

1 14- Mr. J. Glaislier's Remarks on the Weather. 

From the first week in May to tiie second week in June an 
epidemic alFeclion of the throat prevailed among horses. It 
consisted ehieliy of swelliu<j; oi the throat, with sh<)ht fever, 
which continued for a few tiays, anil terminated with profuse 
discharge of thick mucus through the nose. I am not aware 
of its having been fatal in any case. I may sum up and con- 
clude by saying, that we liave had a very favourable "seed 
time," that the land generally s})eaking has been well pre- 
pared, and the weather favourable for cultivation ; that the 
crops look healthy, and that there is every prospect of an 
early and an abundant harvest. 

Rose Hill, Oxford. 

The crops of corn and potatoes are healthy and promising. 

Stonyhurst. The Rev. A. Weld, F.R.A.S. 

The cold east winds in April kept the grass back to such 
a degree, and caused so great a deficiency in the pastures, as 
to give but a very poor prospect of a good hay harvest, and 
induced many farmers to sow a greater amount of grain crops 
than usual. Last year's hay is not to be had in the country. 
The wet weather which prevailed duiing the early part of 
April caused a great delay in the planting of grain crops. 
Oats were first seen about April 10; clover about April 23, 
but was not all sown till May 1. Potatoes were not got in 
till May 2. All these different crops are now looking ex- 
ceedingly well. The crop of beans has been unusually good 
all over the country. I'urnips have been a good deal in- 
fected with the fly; so much so that some farmers had to sow 
a second time. Sheep were washed about May 31, shorn on 
June 10. The late rains have brought forward the grass 
crops with extraordinary rapidity ; they are now heavy, and 
farmers are waiting only for fine weather to mow. Clover 
has been housed, but was light. With this exception, a little 
rye-grass, nothing has yet been cut. 

West Riding of Yorkshire. Charles Charnock, Esq. 

The quarter now passed has been generally very cold and 
dry, and dry soils show in many places a want of rain; pas- 
tures are bare, and meadows are generally light. The season 
is late, both wheat and barley shooting about ten days later 
than in an average season. 

Potatoes are planted very largely, full one-third more than 
usual. I have seen a few instances of the disease, but it is 
very rare; this however is rather early to pronounce the 
danger passed for the season. Of turnips a small breadth 
only has been sown this year, partly from the great breadth 
of potatoes, and pardy from many farmers finding their sheep 
stock at the present prices [^d. per lb.) are unprofitable. Bar- 

Notices respecting Arw Books. 145 

ley is very much varied ; on good land in good cultivation the 
crop is good, but on dry soils it is light and thin. A very 
small breadth of barley is sown this season. Wheat is very 
varied, the crop being from very bad to good according to the 
.soils and management, the drv season havin<>- serious! v affected 
the dry soils. 

An luiusually great breadth of spring wheat lias been sown, 
displacing, as above stated, a portion of the barley crop. 

Stock has generally done well where healthy, but Pneu- 
monia has been very prevalent and fatal in some districls, 
generally among Irish cattle. Potatoes, from the dry cold 
weather, are later than usual. 

XV. Notices respecting New Booh. 

The Course of Creation. By John Andersox, D.D. 
London : Longman and Co. 

E have been much gratified by the perusal of this work, not 
because at the j)resent day physical science, and more espe- 
cially the most poetical of all the branches of it, Geology, requires 
any defence from the reproach of being hostile to religion, but 
because the plain and simple yet forcible and eloquent manner in 
which the records graven upon the stone book of nature are set forth, 
have invested this production with unusual interest ; and the more 
so, as emanating from the jien of a divine fully imbued with the im- 
portant bearings which exist between natural science and revealed 
truth. "The Course of Creation" is no philosophic theory — involves 
no metaphysical inquiry into the origin of things — nor aftbrds any 
new facts connected with the science itself; but is simply intended 
to express the feelings engendered in the mind of the author b)' geo- 
logical pursuits ; and thus it aims to impress others with a desire to 
become acquainted with the works of the Creator and the records of 
His will. 

The subject-matter of the volume consists of the various geological 

phsenomena to be met with in the line of country occurring between 

the Grampians and the Alps ; 'and the relations of the several geolo- 

■ gical formations to each other are treated of in geograpliical sequence. 

Thus we have the general structure of Scotland first mentioned, 
with its series of crystalline, trap and palceozoic rocks, including 
descriptions of the more important animal and vegetable remains 
found in the latter ; to this succeeds the geological structure of 
England with its peculiar and interesting features, from the Silurian 
to the close of the tertiary period ; the concluding geological portion 
is devoted to France and Switzerland, in M-hich we find a concise 
account of the tertiary basin of Paris and the Loire, the volcanic 
district of Auvergne, and the structure of the Alps, &c. 

The descriptions are embodied not only from personal observation, 
but enriched by an extensive acquaintance with, and careful exami- 
nation of, the most recent geological works. 

We only notice one misstatement of any importance which appears 
Phil, Mag. S. 3. Vol. 37. No. 218. August 1850. L 

146 Cambridge Philosoplncal Society. 

to have escaped the author's attention : in speaking of the Swiss 
Ali)S, at p. 295 it is stated, that " the Oxfordian group are repre- 
sented by the ' Neocomian * limestones, a scries of strata abounding 
in fossils of the gault and upper greensand." According to Sir R. 
Murchison, Von Buch, and other geologists, the occurrence of the 
Oxfordian group \vith its characteristic shells is distinctly traced in 
the French and Swiss Alps, and forms the base of all the outer edges 
of the Savoy Alps, overlaid by the Neocomian limestones, which arc 
again surmounted in the Savoy Alps by a dark- coloured limestone, 
which, from its contained fossils, fairly represents the gault and 
upper greensand. 

The concluding part of the work is devoted to general principles, 
in which we find the theories of organic life discussed, especially as 
bearing on the development hypothesis, — the causes of extinction 
of the various forms of animated life which have successively tenanted 
our globe, — the analogical order of moral and physical progression, 
— as well as a chapter on the Mosaic account of creation as recon- 
cilable with geological discoveries ; want of space prevents us from 
extracting the many valuable and eloquent passages contained in 
this portion, involving points of the highest interest. 

To those who have not hitherto investigated the varied and mul- 
tiform changes, both organic and inorganic, to which the superficial 
crust of our globe has been subjected, or have regarded geology as 
an unprofitable and uninviting study, and to the geologist himself 
occupied merely with the laborious task of collecting the dry statical 
details connected with his science, we cordially recommend the per- 
usal of this volume, as unfolding in the plainest manner the beauty, 
harmony and beneficence of Creative power that has reigned through- 
out all past time, and by which the present surface of our earth has 
been elaborated, modified, and adapted to the wants of an intellectual 
and moral being, pointing out to us at the same time, that as an 
inquiry " into the records of Creation, geology has disclosed views, 
and elicited discoveries, of the works of the Divine Architect of the 
world which the religious inquirer will as cordially embrace, as ig- 
norance can overlook or misapprehend." 

XVI. Proceedings of Learned Societies. 


[Continued from p. 69.] 

Feb. 25, /^N the Symbols of Logic, the theory of the Syllogism, 

1850. ^^ and in particular of the Cojjula, and the application 

of the Theory of Probabilities to some questions of evidence. By' 

Professor De Morgan. 

This paper, which is in continuation of the one published in 
vol. viii. part 3 (read Nov. 9, 1846), and of subsequent additions 
contained in the author's work on Formal Logic, is divided into six 

Section I. On the approxhnation of logical and algebraicat modes 
of thought. — The subjects of this section are, — 1st, some development 
of the idea that the oppositions of logic have affinities which may 

Cambridge Philosophical Society. l*? 

one day lead to a connected theory, making use of a common instru- 
ment, just as the oppositions of quantity which are considered in 
algebra are connected by the general theory of the signs + and — ; 
and Snd, some remarks on the resemblance of the instrumental part 
of inference to algebraic elimination. 

Ten such instances as affirmative and negative, conclusive and 
inconclusive, &c., are compared with the logical distinction of uni- 
versal and particular ; and it is pointed out, in all the cases in which 
it is not already acknowledged, that it would be possible to use any 
one of the ten in place of the last. 

Section II. On the formation of symbolic notation for propositions 
and syllogisms. — Exclusive of remarks on the Aristotelian notation 
and on notation in general, and a statement for comparison of Sir 
William Hamilton's notation, this section contains the following 

1. A pictorial or diagrammatic representation of syllogistic infer- 
ences, being after the method pursued by Lambert, with such addi- 
tions as will enable the system to represent all the cases in which 
contraries are used. 

2. An abbreviated and arbitrary method of representing proposi- 
tions and syllogisms. 

Following Sir William Hamilton in making the quantity of both 
subject and predicate matter of symbolic expression, Mr. De Morgan 
gives his system of notation two new features. First, he dispenses 
with the representatives of the terms (except when it may be con- 
venient to introduce them for the time), and represents the proposi- 
tion by the symbols of quantity only, and the presence or absence of 
a sign of negation. Secondly, instead of making the symbols of uni- 
versal and particular absolute, he gives one symbol, ), to a universal 
subject and a particular predicate, and another, (, to a particular 
subject and a universal predicate: a dot [.] signifjdng negation. 
Thus X)-(Y, or simply )•(, represents 'No X is Y': X('(Y, or (•(, 
represents ' Some Xs are not any Ys :' X()Y represents ' Some Xs 
are Ys.' Of the second circumstance above mentioned, Mr. De 
Morgan believes that it makes the rules easier, and knows that it 
makes the notation more suggestive. 

Retaining in mind the order XY, YZ, XZ, which is the oi\\y figure 
used in the classification (being the first with inverted order of pre- 
■ mises), the syllogism is to be denoted by the junction of the propo- 
sitional symbols. Thus )))) = )) denotes ' Every X is Y, every Y is 
Z, therefore every X is Z.' When this is to be read in any figure, 
the subject-quantities are to have their symbols thickened, the second 
premise being read first : thus in the four figures, in order, will be 
seen such symbols as \\, \<^, \\\\, ||j|. 

Section III. On the symbolic forms of the extension of the Aristo- 
telian syste}n in ichick contraries are introduced. — This system is the 
one which w-as completed and published to the Society before any 
correspondence with Sir William Hamilton. Mr. De Morgan re- 
marks that it contains (incidentally, not designedly) every distribu- 
tion of quantifications ; and gives his reasons for not dwelling on this 
fact while the controversy was unfinished, with his statement that it 
had not struck him when the controversy began. Mr. De Morgan 



Cambridge Philosophical Society. 


f E 

Negative ■' ' 





frequently distinguishes ^Ajs system from Sir W. Hamilton's by calling 
the foru^.er that of hitroduvtion of vontrnrips, the latter that of inven- 
tion of j)rc(lic(itcs. For dis^tinctness, it may be stated that Mr. De 
Morpin's other, or numerically dcjinitc sy:<tom (the one concerned in 
tlie discussion), dots not apjx-ar in the present paper, except as matter 
of allusion. 

The forms of predication in this system are as follows, with refer- 
ence to the order XY, x and y being not X and not Y. 

X))Y Every X is Y 

.r))y or X((Y Every Y is X 
X))y or X)-(Y No X is Y 
,r))Y or X(-)Y Everything is X or Y or both. 

X()Y Some Xs ai'e Ys 

.(•()// or X)(Y Some things are neither Xs nor Ys 
X()y or X(-(Y Some Xs are not Ys 
.r()Y or X)-)Y Some Ys are not Xs. 

Various rules of connexion are given, being all translations of 
those in the work on Formal Logic, except a classification of the par- 
ticulars by probability, answering to that of universals. Thus of 
X))Y and X(-)Y, each makes the other impossible : of their con- 
traries X('(Y and X)(Y, each, so far as it affects the other, reduces 
its probability. 

It appears that a quantified term has a quantified contrary : that 
of ' Every X ' is ' some cTS,' &c. 

The symbolic canon of validity is ; — if both middle parentheses 
turn the same way, there need be one universal proposition ; if dif- 
ferent ways, two. Thus )))( and (•))•( both have inferences; and 
so has )•()) ; but )•()( has none. The symbolic canon of inference 
is; — erase all signs of the srdddle term, and what is left (two nega- 
tions, if there, counting as an affirmation) shows the inference. Thus 
from X(-)Y)-(Z we infer X(**(Z or X((Z : more simply, from (•))"( 
we infer ((. 

Section IV. On the symbolic forms of the system in ichich all the 
combinations of quantity are introduced by arbitrary invention of forms 
of predication (Sir W. Hamilton's). 

The modes of predication peculiar to this system have the same 
symbols, )( and (•), as the j)eculiar propositions of the system of 
contraries ; but with very different significations, as follows : — 


(•) Universal negative with 
particular terms, and affirmative 
form in common language. 

All things are either Xs or Ys. 

)( Particular affirmative with 
universal terms, and negative form 
in common language. 
Some thinf/sareneitherXsnor Ys. 

Invention of jJfedicates. 

(•) Particular negative with 
particular terms, not used in 
common language. 

Some Xs are not sotne Ys. 

)( Universal affirmative with 
universal terms, being declaration 
of identity in common language. 

All Xs ore all Ys. 

Cambridge Philosophical Society. 149 

Mr. De Morgan argues that Sir William Hamilton's system cannot 
be called an extension of that of Aristotle, in the sense in which that 
word is used. 

The forms of predication are as follows : — 

A, + A')( All Xs are all Ys I E, )•( No Xs are Ys 
I, SomeXsaresomeYs — (•) SomeXsarenotsomeYs 

A, )) All Xsare some Ys O' )•) No Xs are some Ys 

A' (( Some Xs are all Ys i O, (•( Some Xs are no Ys, 

Previously to entering upon the forms of syllogism, Mr. De Morgan 
repeats and reinforces the objections brought forward in his Formal 
Logic ; namely, that )( is a compound of )) and ((, and has no sim- 
ple contradiction in the system ; and that (•) not onlj^hasno simple 
contradiction, but cannot be contradicted except when the terms are 
singular and identical. He then proceeds to propose one mode of 
remedying these defects. Calling the ordinary proposition cumular, 
he proposes to make it exemplar, as asserting or denying of one in- 
stance only. In the universal proposition, the example is lohoJlij in- 
definite, any one ; in the particular proposition it is not wholly indefinite, 
some one. The defects of contradiction are thus entirely removed, as 
in the following list, in which each universal proposition is followed 
by its contradiction. 

)( Any one X is any* one Y 
(•) Some one X is not some one Y 
)) Any one X is some one Y 
(•( Some one X is not any one Y 

(( Some one X is any one Y 
)•) Any one X is not some one Y 
)•( Any one X is not any one Y 
Some one X is some one Y 

In both systems there are thirty-six valid syllogisms, and in both 
the canon of validity is, — one universal (or wholly indefinite) middle 
term, and one affirmative proposition. But the symbolic canons of 
inference differ as follows (with reference to the order XY, YZ, XZ). 

Exemplar system. — Erase the middle parentheses, and the symbol 
of the conclusion is left: thus ())•) gives (•). 

Cumular system. — Erase the middle parentheses, and then, if both 
the erased parentheses turn the same way, turn any universal paren- 
thesis which turns the other way, unless it be protected by a mark 
of negation. Thus )•(() gives )"•), ())( gives (), and ())•( gives (•(. 

Section V. On the theory qf the copula, and its connexion vnth 
the doctrine of figure. — In his work on Formal Logic, Mr. De Morgan 
had analysed the copula, and abstracted what he calls the copular 
conditions of the relation connecting subject and predicate. These 
are, transitiveness, seen in such copulse as sujjport, govern, is greater 
than, &c., ex. gr. if A govern B, and B govern C, A governs C : and 
convertibilit y,seenin suchcopulse as is acquainted loith, agrees ivith,8ic. ; 
ex. gr. if A agree with B, B agrees with A. Mr. De Morgan's position 
is, that any mode of relation which satisfies both these conditions has 
as much claim to be the copula as the usual one, is, which derives its 
fitness entirely from satisfying the above conditions. So far the 
work cited. In the present paper the correlative copula is introduced, 
as is supported in opposition to supports, &c., and every system of 
syllogism is thus extended. If a copula be taken which is only trans- 

* So that there can be but one X and one Y, and that X is Y. 

150 Cambridge Philosophical Society. 

itive, but not convertible, every sj'llogism remains valid, provided 
that the correlative of that copula be used instead of it, when needful. 
And in this consists, according to Mr. De Morgan, the root of the 
doctrine oi figure. If -|- represent affirmative, and — negative, the 

four figures are connected with + +, H , \- , and (in the 

system of contraries, where negative premises may have a valid con- 
clusion, the fourth figure has equal claims with the rest, though the 
conditions of all the figures are singularly altered). These forms 

do not require the correlative copula : thus -\ in the second figure 

(as Camestres and Baroko among the Aristotelian forms) are as valid 
when the copula is 'supports' or 'is greater than,' as wdien 'is' is 
employed. But in every other case the rule for the proper intro- 
duction of the correlative copula is as follows : — The preceding being 
called the primitive forms of the four figures, when one premise of a 
primitive form is altered, the necessity of a correlative copula is 
thrown upon the other ; when both, upon the conclusion. Thus, the 

l)rimitive form of the .second figure being -\ , and Cesare showing 

1- , it i.s only valid with the copula ' governs,' by making ' is not 

governed by ' the copula of the conclusion, as follows : — 
No Z governs any Y 
Every X governs a Y 
Therefore no X is governed by any Z. 

By an additional letter {g) introduced into the usual words of 
syllogism, the places of the correlative copula may be remembered, 
as in Barbara, Celagrent, &c. : a g being made to accompany any 
member of the syllogism in which the con-elative copula must be 

This theory is applied equally to the Aristotelian system, to Sir 
"William Hamilton's (though not of universal application in the cu- 
mular form), and to Mr. De Morgan's system of contraries. The 
extensions required by the use of a merely transitive copula, in the 
last-mentioned system, are discussed; and mention is made of the 
tricopular system, in which the leading copula and its correlative 
have an intermediate or middle relation, equally connected with 
both ; as in :> = and <: of the mathematicians. 

The next step is the assertion that it is not necessary that any 
two of the three copulse of a syllogism should be the same ; all that 
is requisite is that, in affirmative syllogisms, the copular relation in 
the conclusion should be compounded of those in the premises. The 
instrumental part of inference is described by Mr. De Morgan as the 
elimination of a term by composition {including resolution) of relations, 
which leads to the conclusion that whenever a negative premise occurs, 
there is a resolutiofi of a compound relation. This resolution is shown 
in a case (among others) of the ordinary copula, in M'hich, however, 
it would hardly strike the mind more forcibly than would the pro- 
perties of powers in algebra if every letter represented unity. Mr. 
De Morgan shows (in an addition) that in some isolated cases of in- 
ference which are not reducible to ordinary syllogism, logicians have 
had recourse to what amounts to composition of relations. 

Mr. De Morgan next points out that the copular relation, in 
affirmative projjositions, need not be restricted as applying to one 

Cambridge Philosophical Society. 151 

instance only of the predicate ; and shows that the removal of this 
usual restriction entirely removes all his objections to Sir William 
Hamilton's form of his own system. 

Section VI. On the application of the theory of probabilities to some 
questions of evidence. — This inquiry was suggested by the apparent 
(but only apparent) error of the logicians, who seem to lean towards 
the maxim that, when the subject and predicate are unknown, the 
universal and particular propositions ' Every X is Y,' ' Some Xs are 
not Ys,' are a priori of equal probability. The difficulty is one which 
occurs in the following case : — If a good witness, drawing a card 
from a pack, were to announce the seven of spades, his credit would 
not be lowered, though he Avould have asserted an event against which 
it was 51 to 1 a priori. A common person gives the true answer, 
' Why not the seven of spades as well as any other .'' ' Many readers 
of works on probability would be inclined to say ' That is not the 
question ; why the seven of spades rather than some one or another 
of the fifty-one others } ' The retort is fallacious : it rubs out the 
distinctive marks from the other fifty-one cards, and writes on each 
of them ' not the seven of spades ' as its only exponent. Laplace 
has chosen two problems, in one of which the distinctive marks 
exist, and not in the other ; and, neglecting the consideration of the 
first one, has founded his remarks upon the deterioration of evidence 
by- the assertion of an improbable event, entirely upon the second. 
The object of this section is, by a closer examination of the mathe- 
matical problem of evidence, to ascertain the accordance or non- 
accordance of the results of usual data with usual notions. The 
result of the examination is, that common notions, as in other cases, 
are found closely accordant with theory. For instance, if there be 
n possible things which can happen, so that the mean probability of 

an event is — , a witness of whom we know no particular bias towards 

one mode of error rather than another, asserting an event of which 

the a priori probability is a, has his previous credit raised, unaltered, 

or lowered, according as a — — is positive, nothing, ornegative. So 

that though the a priori probabilities were distributed among a mil- 
lion of possible and distinguishable cases, yet a witness asserting one 
of them against which it is only 999,999 to 1, would have as good 
a right to be believed as though there had been but two equally pro- 
bable cases, of which he had asserted one. 

March 11. — Curvature of Imperfectly Elastic Beams. By Ho- 
mersham Cox, B.A. Jesus College. 

The equation to the curve of an elastic deflected beam is usually 
deduced from the assumption, — 1, that the longitudinal compression . 
or extension of an elastic filament is proportional to the compressing 
or extending force ; 2, that for equal extension and compression the 
compressing and extending forces are equal to each other. 

These hypotheses are not quite correct in practice. All substances 
appear to be subject to a defect of elasticity, i. e. their elastic forces 
of restitution increase in a somewhat less degree than in proportion 
to the extension or compression. If the forces be taken as functions 

I J2 Cambridge Philosophical Society. 

of the hitter quantities expressed by a converging series of their 
ascending integral powers, the terms after the third may in general be 
neglected as of inconsiderable magnitude. If then e be the exten- 
sion of a uniform rod of a unit of Icngtli and a unit of sectional area, 
the longitudinal force producing that extension is 

ae + /3c'^ + jS'e\ 
where a, /3, j8' are empirical constants. 

Simihirly, if c be the compression of a similar rod, the force pro- 
ducing that compression is 

where y, S, h' are three other emj)irical constants. 

These formuhv are to be applied to a uniform beam of rectangular 
section, resting on horizontal supports and slightly deflected at its 
centre. For this purj)ose, the compression and extension of every 
filament of the beam are expressed in terms of the radius of curva- 
ture and the distance from the neutral axis. Analytical expressions 
are thus obtained for the elastic forces developed in any transverse 
section of the beam ; and the position of the neutral axis is obtained 
from the integrals of these expressions by the principle, that the sum 
of all the horizontal forces above is equal to the sum of all the hori- 
zontal forces below the neutral axis. 

Next, the sums of the moments of the elastic forces about the neu- 
tral axis are obtained ; and the sums are equated to the moment 
about that axis of the pressure (P) of the fulcrum, the latter moment 
being the product of half the deflecting weight by the distances {x) 
of the fulcrum from the point of the neutral axis here considered. 
This equation involves the radius of curvature, and is solved with 
respect to the reciprocal of that quantity. It is to be observed, that 
this equation, and also the preceding one determining the neutral 
axis, are not of such a form as to admit of direct solution, and are 
therefore solved by an ordinary method of approximation. 

The reciprocal of the radius of curvature of a point {x, y) of a 
curve is equal to (the second differential of y with resjiect to cr)-f- 
(a quantity which becomes equal to unity when, as here, the incli- 
nation to the axis of x of the tangent at any point of the curve is 
comparatively very small). 

Alaking the substitution indicated, and integrating twice the equa- 
tion last obtained, we obtained finally for the equation to the neutral 
line of a rectangular beam of vertical depth d, and horizontal breadth 
jo,, and length 2a, 

_ Jto;' _ bxT-x"^ (26'^ — cV.r^ _/>'«" _ ^"'"^ i {^b~ — c)a^y?\ 
^~2T3 3.4 4^5 VT" ~3~ 4 j' 


b= I f/(jS + 6V-7-2)(l +«V--0-' 
o a 

hitelligence and Miscellaneous Articles. 153 

If, according to the ordinary hypotheses of perfect elasticity, we 

put a^=y and neglect terms depending on /3, /?', J, J', this equation 

to the elastic curve coincides with that given by Poisson and others. 

If we put x = a, tlie value of the deflection at the centre of the 

beam is 

xa3 _ byra* , (2i-— c)x^a* 
T 4 5 ■ 

Whence it may be seen that the deflection is greater than it would 
be if the elasticity Avere perfect. 

XVII. Intelligeiice and Miscellaneous Articles. 


THE specimen of which the analysis follows, was given me by 
J. W. Foster, Esq., and is the same mineral which has been named 
Coracite by Mr. J. L. Le Conte, and partially described by him in 
the American Journal of Science (New Series, vol. iii. p. 174). As 
it is evident that the conclusions drawn by Mr. Le Conte from his 
qualitative examination were quite incorrect, and as the mineral 
differs considerably, in its reaction with acids, from pitchblende, 
with M'hich it has the greatest analogy, and which at first sight it 
would seem to be, I have carefully examined it, with the following 
results : — 

Substance amorphous ; fracture uneven ; without traces of clea- 
vage ; hardness 3 ; spec. grav. — ; colour pitch-black ; powder 
gray ; lustre resinous. 

Before the blowpipe it does not change its appearance, or fuse, or 
colour the flame. It gives with the fluxes the characteristic reac- 
tions of uranium. 

It dissolves readily without the application of heat in dilute hydro- 
chloric acid, effervescing strongly ; in which respect it differs en- 
tirely from pitchblende, which is insoluble, except in nitric acid or 
in aqua regia. It gives a beautiful green solution, a small quantity 
of flocky silica separating. 

The analysis was conducted as follows : — 

A portion of the mineral, carefully selected and freed from foreign 
matters, was pulverized and dried at 100° C. It was then dissolved 
by hydrochloric acid in a suitable apparatus, the loss of weight being 
considered as carbonic acid. The silica separated by filtration was 
found to be pure when tested by the blowpipe, and was entirely 
soluble in carbonate of soda. In the solution filtered from the silica, 
sulphuretted hydrogen threw down a precipitate, at first dark brown 
and afterwards black, of sulphuret of lead, wliich was estimated as 
sulphate of lead by oxidizing with nitric acid. The filtered solution 
was then digested till it no longer smelt of sulphuretted hydrogen, 
and oxides of uranium and iron and alumina precipitated by caustic 
ammonia. The precipitate was washed with water to which chlo- 
ride of ammonium had been added, and then taken moist from the 

154 Intelligence and Miscellaneous Articles. 

filter and redissolved in hydrochloric acid. In this solution oxide of 
iron and alumina wore precipitated by carbonate of ammonia, the 
oxide of uranium remaining in solution, and care being taken that 
the solution should be quite dilute, in order that the iron might be 
entirely preci])itated. The oxides of iron and alumina were sepa- 
rated by caustic potash. In the solution filtered from these sub- 
stances, the uranium was precij)itated by adding hydrochloric acid 
to supersaturation, boiling to exj^el all the carbonic acid, and then 
adding ammonia. 

In the solution from which the i)rccipitate by ammonia of uranium, 
iron and alumina had been separated, the lime was thrown down by 
ammonia and oxalic acid. Tiie tiltered solution was evaporated to 
dryness, and the ammoniacal salts driven off by ignition, when there 
remained traces of magnesia and manganese. 

The water was estimated by ignition in a bulb-tube, and collecting 
the water driven off in a weighed chloride of calcium tube. The 
mineral docs not however part with any of its carbonic acid at a 
temperature below that required to drive off all the water, nor is it 
rendered less soluble by exposure to the strongest heat of a Berzclius 

No traces of sulphur could be found by boiling the mineral with 
fuming nitric acid, and testing with chloride of barium. 'I'he lead 
has therefore been calculated as oxide, and not as a sulphuret. 
The per-centage results of two analyses are as follows : — 

I. II. 

Sihca 4-35 5-60 

Alumina 0-90 \ ., ^ . 

Oxide of iron 2-24 / 

Oxide of uranium 59-30 ,57'.54 

Oxide of lead 5-36 5*84 

Lime 14-44 13-47 

Carbonic acid 7*47 

Water .. 4-64 

Magnesia and manganese traces 

That the uranium exists in the mineral as U^ O^, and not as 
(JO U- O^, as in the common pitchblende, is evident from its ready 
solubility in acids ; and that the oxide of uranium, or uranic acid as 
it might with equal propriety be called, is in chemical combination 
in the mineral is equally evident, from the fact that its solubility is 
not diminished by ignition. That the silica is also chemically com- 
bined is shown by the fact that it is separated in a state in v.'hich it 
is soluble in carbonate of soda. It is difficult to see in exactly what 
manner these elements are combined with regard to each other, 
though it is probable that the oxide of uranium plays the part of an 
acid toward a portion of the lime (the remaining portion being in 
combination with the carbonic acid) and the lead. The frequent 
occurrence of a small quantitj'^ of oxide of lead with the ores of 
uranium is an interesting fact, on which future investigations may 
perhaps throw some light. — Boston Journal of Natural History, 
vol. vi. p. 37. 

Intelligence atid Miscellaneous Articles. 155 

To the Editors of t/ie PJiilosopfiical Magazine and Journal. 
Gentlemen, Lahore, April 18, 1850. 

I have only an hour or two to spare before the Indian mail leaves 
this, to give you a few notes regarding dust-storms, which are 
very prevalent in this part of India during the dry months of April, 
May and June, that is, before the setting in of the rainy season. 

My observations on this subject have extended as far back as the 
hot weather of IS47, when I first came to Lahore, and the result is 
as follows : — Dust-storms are caused by spiral columns of the electric 
fluid passing from the atmosphere to the earth ; they have an onward 
motion — a revolving motion, like revolving storms at sea — and a 
peculiar spiral motion from above downwards, like a corkscrew. It 
seems probable that in an extensive dust-storm there are many of 
these columns moving on together in the same direction ; and during 
the continuance of the storm, many sudden gusts take place at in- 
tervals, during which time the electric tension is at its maximum. 
These storms hereabouts mostly commence from the north-west or 
west, and in the course of an hour, more or less, they have nearly 
completed the circle, and have passed onwards. 

Precisely the same phsenomena, in kind, are observable in all cases 
of dust-storms : from the one of a few inches in diameter to those 
that extend for fifty miles and upwards, the ph2enomena are identical. 

It is a curious fact, that some of the smaller dust-storms occasion- 
ally seen in extensive and arid ])lains, both in the country and in 
Affghanistan above the Bolon Pass, called in familiar language 
" Devils," are either stationary for a long time, that is, upwards of 
an hour, or nearly so ; and during the whole of this time the dust 
and minute bodies on the ground are kept whirling about into the 
air. In other cases these small dust-storms are seen slowly advan- 
cing, and when numerous, usually proceed in the same direction. 
Birds, kites and vultures, are often seen soaring high up just above 
these spots, apparently following the direction of the column, as if 
enjoying it. My idea is, that the phsenomena connected with dust- 
storms are identical with those present in waterspouts and white 
squalls at sea, and revolving storms and tornadoes of all kinds ; and 
that they originate from the same cause, viz. moving columns of 

In 1S47, at Lahore, being desirous of ascertaining the nature 
of dust-storms, I projected into the air an insulated copper wire 
on a bamboo on the top of my house, and brought the wire into 
my room, and connected it with a gold-leaf electrometer and a 
detached wire communicating with the earth. A day or two after, 
during the passage of a small dust-storm, I had the pleasure of ob- 
serving the electric fluid passing in vivid sparks from one wire to 
another, and of course strongly affecting the electrometer. The 
thing was now explained ; and since then I have by the same means 
observed at least sixty dust-storms of various sizes, all presenting 
the same pha^nomena in kind, 

I have commonly observed that, towards the close of a storm of 
this kind, a fall of rain suddenly takes place, and instantly the stream 

156 lutcUigoicc and Miscellaneous Articles. 

of electricity ceases, or is much diminislicd ; and wlien it continues, 
it seems only on occasions, when the storm is severe and continues 
for some time after. The barometer steadily rises throughout. In 
this i)art of the world, the fluctuation of the barometric column 
is very slight, seldom more than two or three-tenths of an inch at 
a time. 

The average height at Lahore is T ISO, corrected for temperature, 
indicating, I suppose, above 1150 feet above the level of the sea, 
taking 30 inches as the standard. 

A large dust-storm is usually preceded by certain peculiarities in 
the dew-point, and the manner in wliich the particles of dew are de- 
posited on the bulb of a thermometer. My mode of taking the dew- 
point isj to plunge a common thermometer in a little ice, let it run 
down 20° or 30°, take it out, wipe it dry, hold it up to the liglit, and 
observe the briglit spot, and continue to wipe off the dew so long as 
it is deposited and dulls the bulb : at the instant it clears off mark 
the temperature. This I have compared frcquentlj' with Daniell's 
hygrometer, cooled by means of chloroform, and find them both 
correspond with the greatest accuracy. 

This is a digression ; but I have no time to arrange, and must 
therefore put down my remarks as they occur to me. 

The dew-point varies very much, but is usually many degrees below 
the temperature of air, 20° to .50° or more. 

It also varies according to the time of year. During November 
last the mean temperature of dew-point was about 47°, that of the 
air about 71°. 

In January 1850, dew-point 43°; in the air, 61°; and the mean 
temperature of self-registering thermometer 45^'4. 

In February 1850, mean of dew-point 48°, and air 64°'5. 

April 1850, mean temperature of dew-point so far is about 60°, 
and the air 84°. 

The sparks or the stream of electricity, as it is seen passing from 
one wire to the ether, is in some cases, and during high tension, 
doubled or trebled ; and is never straight, but invariably more or 
less crooked. 

Various kinds of sparks are seen at times ; one end of the wire 
has a star ; and from the wire, when held just beyond striking di- 
stance, a brush is seen curved, which, when viewed through a lens, 
seems comjiosed of a stream or curved brush of bright globules, like 
a shower of mercury. 

The manner in which the electricity acts upon the dust and light 
bodies it meets within its passage, is simple enough. I suppose the 
particles similarly electrified and mutually repulsive, and then, 
together with the whirling motion communicated to them, are 
whisked into the air. The same takes place when the electricity 
moves over water. The surface of the Avater becomes exposed to 
the electric agency ; and its particles, rendered mutually repulsive, 
are in the same way whirled into the air. 

At sea the waterspout is thus formed. First of all is seen the 
cloud descending, and beneath may be observed the water in a cone, 
misty and agitated ; soon the cloud is seen to approach and join the 

Intelligence and Miscellaneous Articles. 157 

latter, involving both extremities in one column, having a spiral 
motion, and on it moves or continues stationary. The power of 
electricity in raising bodies, when combined with thispecuUar whirl- 
ing motion, will account for fish, &c. being carried up in its vortex 
and afterwards discharged to a distance on the earth. The motion 
of the dust-storm may be described by spinning a tee-totum on a 
drop of ink ; and the way in which bodies are projected may be in 
like manner described, by letting fall a drojJ of ink on the centre 
of a tee-totum while spinning. In this case the particles of ink are 
thrown off at tangents ever varying, as the centre moves ; and per- 
ha])s it will be found, that when these kind of storms pass through 
forests, trees uprooted are distributed something in this manner. 

The violent dust-storms are by some supposed to commence at the 
foot of the hills. I cannot tell if this be the case or not, but should 
think that they do not necessarilj^ do so, as many often originate in 
extensive arid plains; and the rarefaction of air, from great and long- 
continued heat, may be in some way connected with the exciting 

Some of them come on with great rapidity, as if at the rate of 
from 40 to 80 miles an hour. They occur at all hours, oftentimes 
near sunset. 

'I'he sky is clear, and not a breath moving ; presently a low bank 
of clouds is seen in the horizon, which you are surprised you did 
not observe before ; a few seconds have passed, and the cloud has 
half filled the hemisphere : and now there is no time to lose — it is a 
dust-storm, and helter-skelter everyone rushes to get into the house 
in order to escape being caught in it. 

The electric fluid continues to stream down the conducting wire 
unremittingly during the continuance of the storm, the sparks often- 
times upwards of an inch in length, and emitting a crackling sound : 
its intensity varying upon the force of the storm, and, as before 
said, more intense during the gusts. 

Many dust-storms occur at Lahore and in the Punjaub, generallj' 
during the hot and dry months, as many as seven and nine in one 

One that occurred last year in the month of August seemed to 
have come from the direction of Lica, on the Indus, to the west and 
by south of Lahore, and to have a north-easterly direction. An 
officer travelling, and at the distance of twenty miles or so from 
Lica, was suddenly caught in it ; his tent was blown away, and he 
himself knocked down and nearly suffocated by the sand. He stated 
to me that he was informed by one resident at Lica, that so great 
was its force at the latter place, as to crack the walls of a substantial 
brick dwelling in which the above officer had lately resided, and to 
ujiroot some trees about. 

'I'he instant the insulated wire is involved in the electric current 
marked by the column of dust, down streams the electricity. 

I have sometimes attempted to test the kind of electricity, and 
find that it is not invariably in the same state ; sometimes appearing 
-|-, at other times — , and changing during the storm. 

One day I caused the current to pass through a solution of cya. 

158 Litclligence and Miscellaneous Articles. 

nide of silver, so as to affect a small piece of copper, which was ra- 
pidly covered with a coating of silver, which upon drying peeled off. 
In this case the cyanide of silver was pure, without any salt ; but 
in subsequent attem])ts to silver a wire in this way, I have not suc- 
ceeded, only a very slight deposit taking place, which was not in- 
creased by long exposure to the influence. 

But in all the cases I tried subsequent to the one first alluded to, 
the oxide of silver was dissolved in cyanide of potassium. In the 
course of time bright and minute crystals were formed, transparent 
and colourless, on a co])pcr coin. Yours truly, 

P. 13addeley, 
Surgeon-Assistant, Lahore. 


If a somewhat strong capillary tube, closed at one end and drawn 
out at the other to a slender point, is filled with water at the tem- 
perature of 28° or 30° Cent. ; if this tube is cooled down to 18°, so 
as to cause a certain quantity of air to enter it at the open point, and 
it is then closed, and again heated to 28° and gradually higher, after 
a certain time the air is comjiletely dissolved. If cooled to 18°, the 
original temperature at which the tube contained at the same time 
gas and liquid, it is seen that the water continues to occupy the 
whole of the internal capacity, and maintains thus an invariable 
density between 28° to 18°. Its temperature may even be lowered 
s;:ill more. At this moment the least shock or collision, the least va- 
riation causes the instant reappearance, with a sort of ebullition, 
a slight noise, and a shock more or less perceptible, of the gas dis- 
solved in the water. It dilates rapidly, and in less than a second 
has resumed its primitive volume at 18°. I have made the same 
observations with the following liquids, selected from all classes : — 
water, solutions of various salts and gases, solution of soda, various 
acids, alcohol, sether, acetone, Dutch liquid, essence of turpentine, 
oil of olives, creosote, sulphuret of carbon, chlorides of metalloids 
and metals, bromine. Mercury is the only liquid with which I have 
not succeeded, either in the presence of the air or in vacuo. A 
bubble of air remained several days in presence of the mercurj'' with- 
out dissolving, at least completely, and that under pressures of 200 
to 300 atmospheres, produced by preventing, for that length of time, 
the dilatation of the mercury due otherwise to an increased tempe- 
rature of 8° or 10°. 

In these phaenomena there are two things very distinct. 1 . An 
unstable supersaturation of the liquid by the gas, produced under the 
influence of the pressure. There are numerous examples of this 
order of facts. 2. A state of forced dilatation of the liquid : the latter, 
in fact, an instant before the vibration, fills the volume which the gas 
occupies an instant after conjointlj' with it, and this volume is the 
same which the dilated liquid filled on an elevation of temperature 
of 8 to 10 degrees and more. The variation of density thus produced 
is enormous ; for water it is equal to -j^ of its volume at 18° ; for 
alcohol to ~^, for aether to -J^. Such an effect would be produced 
in an opposite direction only by a pressure of 50 atmospheres for 

Meteorological Observations. 159 

water, of 150 for aether. This phariomenon is very general, as is 
proved by the variety of the liquids on which I have operated. It 
probably accompanies all supersaturations, but at variable degrees 
and in various directions, without being capable of being proved. 

Following the advice of M. llegnault, I endeavoured to separate 
the two facts, and to produce the dilatation of the liquids in vacuo. A 
peculiar apparatus enabled me to fill the tubes with liquids absolutely 
freed from air, and to close them M'ithout letting any gas enter. 
Under these new conditions, I reproduced the phsenomenon of forced 
dilatation with water and aether, and have thus seen that it is inde- 
pendent of supersaturation. This permanence of the density of the 
liquids in an interval of temperature more or less considerable, ap- 
pears to me attributable to the adhesion of the glass and the liquid : 
it is a force which is opposed to the division of this latter, and which 
can only be destroyed by an increase of the molecular attraction of 
the liquid for itself, an increase produced under the influence of cool- 
ing. — Comptes Rendus, June 24, 1850. 


Ckiswick. — June 1, 2. Very fine. 3, 4. Fine, but air excessively dry. 5. Slight 
haze: sultry. 6. Overcast : rain. 7. Cloudy and boisterous : showery. 8. Dull 
and cloudy : fine. 9 — 11. Very fine. 12. Fine: cloudy. 13. Cloudy: clear 
14. Uniformly overcast: rain: showery. 15. Rain: clear at night: frostj/' 
16. Clear : cloudy and fine. 17. Very fine. IS. Cloudless : very dry air : large 
distinct halo round the sun at noon. 19 — 22. Very fine. 23. Hot : quite cloud- 
less. 24,25. Hot, with slight dry haze. 26. Hazy : hot and sultry : heavy rain 
at night. 27. Rain : fine. 28. Hazy: rain. 29. Cloudy : very fine : clear and 
cold. 30. Fine : cloudy. 

Mean temperature of the month 59°"26 

Mean temperature of June 1849 59 "SO 

Mean temperature of June for the last twenty-three years ... 60 '88 

Average amount of rain in June 1*88 inch. 

Boston. — June 1. Cloudy. 2 — 5. Fine. 6,7. Cloudy: rain p.m. 8,9. 
Cloudy. 10,11. Fine. 12,13. Cloudy. 14. Cloudy : rain a.m. and p.m. 15, 
16. Cloudy. 17. Cloudy : rain, with thunder and lightning a.m. 18,19. Fine. 

20. Cloudy. 21. Fine. 22. Cloudy. 23. Fine. 24. Fine: thermometer 88° 
2 o'clock P.M. 25 — 27. Fine. £8. Fine : rain a.m. and p.m. 29,30. Cloudy. 

Applegartk Manse, Dumfries-shire. — June 1. Fine : fair : very warm. 2, Fine : 
very warm. 3. Fine : getting cloudy. 4. Fine : still cloudy. 5. Shower a.m.: 
thunder. 6. Shower a.m. : heavy rain p.m. and thunder. 7. Showery a.m. : 
fair p. .VI. 8. Showery all day. 9. Fair, but getting cloudy. 10. Slight shower 
early : fair p.m. 1 1. Slight shower-early : fine day. 12. Rain and wind all day. 
13. Rain during the night: fair all day. 14. Rain nearly all day. 15. Fair all 
day and fine. 16. Fair and fine: cloudy p.m. 17. Rain early; fine day. 
18. Fine all day. 19. Cloudy, but fine. 20. Fair and fine : getting moist p.m. 

21. Showery. 22. Cloudy: rain during night. 23 — 25. Very fine all day. 
26. Very fine : fresh and invigorating. 27. Parching east wind. 28. The air 
highly electric. 29. The air highly electric : a few drops. ,30. Rain p.m. ; con- 
tinued all night. 

Mean temperature of the month 57°'6 

IMean temperature of June 1849 53*3 

Mean temperacure of June for twenty-eight years 55 '9 

Rain in June for twenty years 3'16 inches. 

Sandwick Maiise, Orfc/iei/. — June 1. Fine, 2, 3. Fine : warm. 4. F'ine. 5. 
Rain: fog. 6. Damp: cloudy. 7. Drops: showers. 8. Drops. 9. Drops: 
rain. 10. Fine : rain. 1 1. Showers : clear. 12. Rain : showers. 13. Drizzle: 
showers: drizzle. 14. Bright: drops. 15. Bright: clear. 16. Fine: clear: 
fine. 17. Fine. 18. Fine : cloudy. 19. Cloudy. 20. Showers : cloudy. 2i. 
Rain : thunder: showers. 22. Bright: rain. 23. Cloudy. 24. Bright : clear. 
25,26. Cloudy. 27. Bright: cloudy. 28. Bright: clear. 29,30. Bright: 



^ o 00 -^ ^< ^ 

O -« CO— <N O 

'. S 5 ^ .• & f. ^ . c c « fe ^ ^ ^ «• „• ^ =. I a< ■ ^ 3; 

; ^ 

? =; Sf S S ^ ^' i ■! i &■ «' i Sf' c «; <^ B:* -I -I ■:' i i^ ^ i \ «5 ^' ^' 

•ui-d I 

1 'JiaiMsiijo 


C * 






i'^ '^'^ '^iiii'^ ^ i ^ i « i i ^ d « i ^i^^^^^i i 

r<5C>ost^c^-^'-oc«'r)— CNOOlOlnooo^cs^Olra^^lfb^^Of^^— < — 00— " 
coc^iiotOLO^ciio-^oooco— — OM^OMnroa\ot^(C'^'*— cocoro'* — 


voodb — 0^r~OOO^COlft^odbc^^o<M 0<MOaNvbOM-^CO<N(NrO»hoOO 

lOioLcvotoO'O^oio^O'oiOioiOLOiovO'O'oysvoioiot^r^t^ovo >o^ 

Oco>-0 0^— 'lOOO(^^LOOooo^■^^ooot^'»lOr~cot^C^O^^tr>C^o^^o— 'CO 

O O O O C^C^O^O>w^^o^o^O^C^O^O^O O O 0^0^0^0 C O O^O C^O^O^ 
COC'5C'3tOC)0<<MOIO><M(NC<C>10le4C<C-50COCJC4 0JC'5COrOO«C--5CNOI(N 

uoiocoot^OMS>oioco>ocoioo— 000 


e«cocO'7>OMp<N>paoco>p<^o— >Loc^o^o — <: 
O O O O o^o^c?^0^0^0^0^0^0^0^0^&^0 O O 0^0^0^0 O O 0\ O 0^0^0^ 




0^ CTi 0^ 0^ 0^ 0^ 0> O^ C^ 0> 0^ Ot 0^ 0^ 0^ 0^ C^ C^ On 0> On On On 0^ On On 0^ On On CN 

) 01 30 -^ < 
> CJ O 30 > 

— o 

— 00 

CI o 

6 6 


-- _ o 

rl> (M O 

6 6 6 


ON r^ o 

ON 10 o 
lO t^ o 

3D UD >0 

I ON 00 O 
I ON — — 

c< c^ 

^ o 
■^ 10 

ON C l^ 

p O CI 

ON ON 6 6 6 

d ON — -^ O 

T >o 'S' ^r ON 
r^qc 9 — CI 

ON ON 6 6 6 

01 d CO COi CO 

ON t^— ' I 
CO 33 CI I 
CO — — • 

6 6 6 < 


CO CI — 

>0 lO -^ 
O LO -* 

O — CO — 

O 10 00 CO 

CO ON>p 

6 ON ON On 

1 CO d d CI 

To -^00 d\ 


— ON O 00 

00 CO 
t-- ON 

00 c^ 

10 -^ 

00 ON 

_/^IC0'^U0>Ct^00ONO — dC0'3•U0<Ot^Q0O^O— dC0-^lO«t^00CNO 

— i'-<'->«r---r-F-r-l^dClddddddddCO 

<=< @ (=> o 







XVIII. On the Composition of Beudantite. 
Bij John Percv, M.D., F.R.S."^ 

LEVY first described this mineral, and from his own ex- 
amination of its physical characters, and Wollaston's 
determination of its composition, pronounced it to be a distinct 

The following is Levy's description, the measurement of the 
crystals being omitted. 

"This substance occurs in small crystals closel}' aggregated, 
of which the form is a slightly obtuse rhombohedron, with the 
summits truncated. Their colour is black at the surface, and 
their lustre somewhat resinous; but their fragments are trans- 
lucent, and of a deep brown colour. The hardness is sensibly 
greater than that of fluate of lime. When pounded, the 
colour is of a greenish-gray. The matrix seems to be the 
same substance in an amorphous state with veins of fibrous 
hematite; it comes from Hornhausen on the Rhine. I am 
indebted to Dr. WoUaston f[)r the chemical examination of 
this mineral, the result of which is very interesting; the only 
substances he has been able to detect in it being oxide of lead 
and oxide of iron." — Annals of Philos. N. S. vol. xi. p. 195. 

Recently, Descloizeaux has examined the crystallographic, 
and Damour the chemical properties of Beudantite [Ann. de 
Ch. et de Phys. t. x. p. 73, 3'^°^^ S.). The crystals upon 
which they operated were taken from a specimen in the col- 
lection of the Ecole des Mines at Paris, and were of two 
kinds, green semi-transparent cubes, and bright black cubes, 
as seen by reflected light. Damour asserts that the former 
were composed of arsenic acid, oxide of iron and water, and 

* Communicated by the Author. 
Phil, Mag. S. 3. Vol. 37. No. 249. Sept. 1850. M 

162 Dr. Percy on the Composition of Beudantitc. 

were identical both in physical and chemical properties witii 
cube-ore; and iliat the latter were principally composed of 
hydrated arseniate of sesc]uioxide of iron containing- in acci- 
dental mixture oxide or sulphuret of lead. 

Mr. Brooke having- supplied me with some of Levy's 
oriirinal specimen of Beudaniite, from which the portion ex- 
amined by Wollaston was taken, I am now able to present 
quantitative analyses of this mineral. As, however, the quan- 
tity placed at my disposal was comparatively small, and as 
Wollaston mentioned only the })resence of oxide of iron and 
lead, I shall consider it necessary to stale somewhat minutely 
the results of my examination. It will be seen, by referring 
to Levy's description previously inserted, that only the black 
crystals of Descloizeaux agree with that description. 

Qiialitative Analysis. 

1. Heated in the closed tube, colourless liquid was given 
off, which reddened litmus-paper, and produced a white pre- 
cipitate in a solution of chloride of barium. 

2. A yellow-brown bead was obtained by beating with 
borax in the outer flame of the blowpipe. 

3. By heating on charcoal in the inner flame with carbonate 
of soda and a little borax, a dark-coloured bead was produced, 
from which, by trituration and laevigation, numerous brittle 
metallic particles and a disc of soft metal like lead were ob- 

4. By roasting the metallic particles (3.) in an inclined open 
tube, the characteristic odour of arsenic was instantly per- 
ceived, and a very sensible quantity of white crystalline sub- 
limate was formed. 

5. The disc of soft metal (3.) dissolved without residue in 
dilute nitric acid. The solution, evaporated to dryness, gave 
a white crystalline residue, in the aqueous solution of which 
iodide of potassium produced a voluminous deep yellow pre- 

6. The mineral completely dissolved in hydrochloric acid 
by the aid of heat, forming a brown solution like that of ses- 
quichioride of iron. 

7. Solution (6.) was not rendered turbid by dilution with 

8. Solution (6.) gave a red-brown precipitate with ammonia, 
like sesquioxide of iron. 

9. Solution (6.) gave a black precipitate with sulphuretted 
hydrogen in excess. 

10. Solution (6.) gave a very sensible white precipitate with 
chloride of barium, not redissolved by dilution with water. 

Dr. Percy on the Composition of Beudantite. 163 

11. By Reinscli's test (electrotype copper being used), so- 
lution (6.) nave ample evidence of the pre-.ence ot arsenic. 

12. The mineral was fused with a mixture of carbonate of 
potash and soda. The product was washed with boiling 
water, when a clear colourless solution and a brown residue 
were obtained. 

13. Reinsch's test applied to solution (12.) detected arsenic; 
by heat in an inclined open tube, the gray coating was re- 
moved, and a white, sparkling, crystalline sublimate obtained. 

14. Marsh's test applied to solution (12.) also gave unequi- 
vocal evidence of the presence of arsenic in considerable 

15. Solution (12.) was rendered acid by hydrochloric acid, 
and treated with sulphuretted hydrogen. The precipitate was 
digested with the strongest nitric acid ; the solution was filtered, 
reduced by evaporation, and treated in Marsh's apparatus, as 
modified by the Prussian government (Chem. Gaz. vol. iii. 
p. 46), when an abundant deposit of metallic arsenic was ob- 
tained. This was converted into white sublimate, which was 
rendered yellow by sulphuretted hydrogen. 

16. To the solution (15.) left, after separation of sulphuret 
and free sulphur, and reduced by evaporation, hydrochlorate 
of ammonia, and sulphate of magnesia were added. Alter some 
time numerous crystalline particles appeared on the surface 
of the liquid, and on the sides and bottom of the glass vessel. 
This crystalline precijiitate, tested with molybdate of ammonia 
(Svanberg's process), gave a yellow precipitate. 

17. The solution of the mineral in hydrochloric acid was 
treated with excess of ammonia and then digested with hydro- 
sulphate of ammonia. The precipitate was treated with strong- 
nitric acid. Sulphuretted hydrogen was passed through the 
diluted acid solution, which was afterwards filtered and boiled 
with nitric acid. Excess of ammonia was added. The pre- 
cipitate was heated with carbonate of soda and nitrate of 
potass on platinum before the blowpipe, but no green colo- 
ration was produced. 

18. The precipitate by ammonia (17.) was boiled with 
potash. The potash solution was rendered acid by hydro- 
chloric acid, and afterwards alkaline by ammonia, but no 
sensible precipitate followed. 

19. The brown residue (12.) was dissolved in hydrochloric 
acid. Sulphuretted hydrogen was passed through the solu- 
tion, which was aiterwards filtered and boiled with chlorate 
of potash. Ammonia was added. The filtrate was tested with 
oxalate of ammonia, but no turbidity followed, 

20. The filtrate (19.) was tested with phosphate of soda, 

M 2 

164- Di-. Percy on the Composition of Bcudantite. 

but, alter long standing, no trace of crystalline precipitate 

First Analysis. 

In this analysis the crystals employed were not selected 
under a lens, and were mixed with some amorphous brown 

Weight of mineral after drying at ISO'^ C, 6*17 grains. 
The colour of the powder was light brown. 

It was fused witli more than 20 grains of a mixture of car- 
bonate of potash and soda. The product was thoruughly 
washed with hot water and the solution filtered. 

Solution {a) and Residue [b) 

Solution [a). Colourless. Excess of hydrochloric acid was 
added. It was then boiled with a little sulphite of potash, 
after which sul[)hui"etted hydrogen was passed through it. A 
reddish-brown precij/itale was produced, which after standing 
all night in a warm place, was covered with a fine yellow pre- 
cipitate. Some lead had evidently been dissolved by tl)e ex- 
cess of alkaline carbonate*. The precipitate was washed with 
water anil atterwards digested with iiydrosulphate ofammonin. 

A minute quantity of black matter remained undissolved 
upon the filter, upon which the sulphuret of lead subsequently 
separated from the insoluble residue {b) was collected. 

The filtrate was treated with excess of hydrochloric acid, and 
left in a warm place more than twenty-four hours. The pre- 
cipitate, which evidently consisted chiefly of free sulphur, was 
analysed in the usual way for arsenic. Weight of precipitate 
after drying until it ceased to lose weight, 2'08 grains. It 
was boiled vviih the strongest nitric acid. Globule of free 
sulphur, washed and dried, weighed 0*65. To the acid so- 
lution excess of chloride of barium was added. The sulphate 
of baryta obtained, washed, dried and ignited, weighed 7"55. 

The solution, iVom which the arsenic had been precipitated 
as sulphuret, was reduced to a small volume by evaporation. 
Sulphate of magnesia, hydrochlorate of ammonia, and am- 
monia were then added. The crystalline precipitate was 
washed on the following morning with cold ammonia-water. 
Dried and ignited it weijrhed 0-14 qv. 

Residue (b). It was dissolved in hydrochloric acid. Sul- 
phuretted hydrogen was passed through the solution. The 
precipitate was collected on the filter before-mentioned. It was 
digested with the strongest nitric acid, a little sulphuric acid 

* I have found that when a solution of carbonate of potasli is long kept 
in ajimtglass Lottie, it dissolves a very sensible amount of lead. 

Dr. Percy o)i the Composition of Beudantite. 165 

was added, and the whole evaporated to dryness and ignited. 
The product weii^hed 2*05 grs. 

The solution from which the lead had been separated was 
boiled with chlorate of potash. Ammonia in excess was 
added. The precipitate, washed, drietl and ignited, weighed 
2-62 grs. 

Second Analysis. 

The particles of crystals were carefully selected under a lens. 

Weight 6'6'\i grains. 

The mineral was digested in hot hydrochloric acid. Excess 
of ammonia was ailded to the solution, and atterward^i excess 
of hydrosulphate of ammonia, when the whole was exposed to 
a gentle heat during many hours. I'he precipitate was washed 
on a filter with water containing a little hydrosulphate of am- 
monia, and afterwards treated with hot hydrochloric acid. 
Decomposition was complete. Through the solution, after 
filtration, sulphuretted hydrogen was passed for a considerable 
time. The precipitate was digested with the strongest nitric 
acid, and after the addition of a few drops of sulphuric acid, 
evaporated to dryness and ignited. The product weighed 
2*66 grains. 

The solution from which the lead had been separated by 
snl|)huretted hydrogen was left in a warm place until the 
odour of that gas ceased to be detected. It was filtered, 
boiled with nitric acid, and treated with exce«s of ammonia. 
The precipitate, washed, dried and ignited, weighed 2'50 grs. 

The hydrosulphate of ammonia solution was digested with 
excess of hydrochloric acid in a warm place for more than 
twenty-four hours. The precipitate, washed and dried at 100" 
C, until it ceased to lose weight, weighed 3*72 grs. The 
arsenic was determined indirectly in the usual way. The 
analytical data obtained are as follow : — 

Sulphur and sulphuret analysed, weighed . . . S'tl 
Ditto ditto, adherent to filter . . ^ . 0*31 

Globule of free sulphur 1*27 

Sulphate of baryta 11*60 

The solution from which the arsenic had been separated as 
sulphuret by hydrochloric acid, was reduced by evaporation, 
and treated with excess of chloride of barium. Tiie preci- 
pitate, washed, dried and ignited, weighed 2'4-0 grs. 

Of another portion of crystalline fragments selected under 
a lens, SvSi grains were weighed. 

The mineral was digested in hot hydrochloric acid. The 
solution was poured into a hot solution of chloride of ba- 

166 Dr. Percy on the Composition of Bettdantite, 

riuni. The precipitate, washed, dried and ignited, weighed 
2-00 grs*. 

Loss by colcination, determination of arsenic, — 3" 54 grs. of 
the mineral reduced to powder were hented in a small closed 
tube ol Bohemian glass for a considerable time ; first over the 
spirit-lamp, and afterwards at a bright red heat before the 
blowpipe. The loss in calcination was 040, the calcined 
mineral wei<ihinij i5*14' ;j:''s. This residue was red-brown, like 
sesquioxide of iron. It was dissolved in hot hydrochloric acid, 
and chloride of barium was added to the solution. The pre- 
cipitate, washed, dried and ignited, weighed 090 gr. 

The solution was Ireed from baryta by sulphuric acid: ex- 
cess of amnu)nia was addetl, and afterwards hydrosulphate of 
ammonia. The determination of the arsenic was made as 
previously describeil. The analytical data are as Ibllovv: — 
Sulphur and sulphuret analysed weighed 3*13 
Sulphur and sulphuret adhering to filter 0"07 

Free sulphur 0*50 

Sulphate of baryta 17'24 

Determination qfSulp/iuric Acid in part of the same specimen 
of mineral used in the last determination. 
2*40 grs. were dissolved in hydrochloric acid. Chloride of 
barium was added. The precipitate, washed, dried and ig- 
nited, weighed 0*83 gr. 

Results Tabidated. 

First Analysis. 
Weight of mineral 6*17 grs. 

Arsenic by loss 0-39 = 6*32 per cent. =9-68 (As O^). 
Phosphate of magnesia 0-14 = -09 (PO^) =1'46 per cent. 
Sulphate of lead 205 = 1-51 (PbO) =24-47 per cent. 
Sesquioxide of iron 2*62 = 42'46 per cent. 

Second Analysis. 
Weight of mineral 6'64 grs. 
Sulphate of lead 2-66= 1*96 (PbO) =29-52 per cent. 

* On the Separation of Sulphuric Acid from Su'pJiate of Lead by Chloride 
of Barium. — As the mineral under examination containe'l siil|)liiinc acid and 
oxide ot'lead, the correctness of tiie preceding deterniination of sulphuric 
acid was tested by the following experiment. Of siilphnte of lead, which 
had been prepared some ye-.irs previously, and of the absolute purity of 
which I was not certain, 2o'92 grains were weighed after heating, and dis- 
solved in hot iiydrochloric acid. The acid solution was poured into a hot 
solution containing more ihan 20 grains of chloride of harium. The sul- 
phate of baryta, washed, dried and ignited, weighed 1804. Now 23-92 of 
sulphate of lead contain of sulphuric acid 620, and 1804 of sulphate of 
baryta contain of sulphuric acid 632. These results are sufficiently sa- 

Dr. Percy on the Composition of Bciidantite. 167 

Sesquioxide of iron 2*50 = 37*65 per cent. 

Arsenic by loss 0-59 = S-88 per cent. = 13*60 (As O"^). 

Sulphate of baryta 2-4-0 = 0-82 (S0^) = 12-35 per cent. 

Sulphuric Acid. 

Wei<^ht of mineral S'SI- grs. 

Sulphate of baryta 2-00 = 0-69 (S03) = 12-92 per cent. 

Water, Arsenic and Sulphuric Acid. 
Weight of mineral 354 jjrs. 
Loss by calcination 0'4-0=ll'30 per cent. 
Sulphate of baryta 0*90 = 0-31 (SO^) = 8*76 per cent. 
Arsenic by loss 26 = 7'34 per cent. =11-24. (As O^). 

Determination of Sul})huric Acid in another portion of the same 
specimen as used in the Inst determination "without calcination. 
Weight olnnneral 2-40 o;rs. 

Sulphate of baryta = 0-83 = 0*28 (SO^j^ 11-67 per cent. 
Loss of sulphuric acitl in calciuaiion is 11-67—8-76 = 2-91 

per cent. 
Water, therefore, is 11*30 (loss by calcination) — 2-91 (loss 
of sulphuric acid by calcination) =8-49 per cent. 

I. II. 



Oxide of lead . . 

. 24-47 




Sesquioxide of iron 

. 42 46 




Sulphuric acid 

. 12-31* 




Arsenic acid . . 





Phosphoric acid 



not detei 


Water . , . . , 





98-87 101-61 

The preceding results prove that Beudantite is chiefly com- 
posed of sesquioxide of iron and oxide of lead, and so far con- 
firm the acciuacy of Wollaston's examination of it. They 
also confirm Damour's stfitement of the presence of arsenic 
and sulphur, and further demonstrate the presence of phos- 
phoric acid. But the sulphur cannot, as Damour supposes, 
exist even in part as sulphuret, because the mineral dissolves 
without residue in hydrochloric acid; whereas if a sulphuret 
were present, there would be a residue of free sulphur, the 
result of the action of the sulphuretted hydrogen evolved by 
the decomposition of the sulphuret upon the sesquichloride 
of iron formed at the same time. 

* Mean of three determinations. 

t I think it probable that this tletermination of arsenic is very sensibly 
excessive. I have not given the mean of the several determinntions, be- 
caii!>e 1 wished to put together the results obtained in the analysis of one 
portion of the naineral. 

l(jS Dr. Percy on the Composition of Bendautite. 

The (jiiantitative results nre less satisfactory than the qua- 
litative. The (nff'erence between the projioriions of oxide of 
iron and oxide of lead in the two analyses is considerable; 
but the Ibllowing facts may serve in part to exj)lain this dis- 

In the first analysis, the crystalline fragments were not 
selected under a lens, and were mixed with some of the amor- 
phous brown matrix; while in the second, the pure crystal- 
line fragments were alone selected under a lens as carefully 
as possible. Besides, the portions of mineral used in the two 
analyses w'ere taken from different parts of Mr. Brooke's 
specimen, and were received by me at different times. 

The differences also between the several determinations of 
arsenic are considerable; but, irrespi'ctive of the probable 
variation in composition of the several jiortions of mineral 
submitted to analysis, it is not to be expected that in analyses 
of such small (]uaiitilies of matter as three or six grains, 
arsenic should be detei'mined with precision. And the same 
may be said of the determinations of phosphoric acid. It is 
inferred that the arsenic exists as arsenic acid. 

I wish it to be particularly understood, that I do not pie- 
tend to present these analytical results as more than approxi- 
n)ate; for although I observed every precaution in the investi- 
gation, yet in the analyses of such a conjplex mineral as Beu- 
dantite, precision is not to be expected unless a lai"ger quantity 
is operated on than I had at my disposal. 

The oxide of lead appears to exist in combination with sul- 
phuric acid, because in the mineral which has been strongly 
heated, sufficient sulphuric acid remains to saturate the oxide 
of lead. Thus 8*76 per cent, of sulphuric acid was found in the 
mineral after having been strongly heated, while before it con- 
tained ir67 percent. Now 8"76 of sulphuric acid contain 
5*24 oxygen. The oxygen of the oxide of lead in the first 
analysis is 1'75, or precisely one-third of that of the acid ; that 
is, in the ratio which exists between the oxygen of the base 
and that of the acid in neutral sulphate of leatl. In the second 
analysis it is less than one-tliird; still the difference is within 
the limit which, in the present case, may fairly be assigned to 
error of analysis. 

Again, the sulphuric acid could only be combined in small 
proportion with oxide of iron; for otherwise a much larger 
quantity of acid must have been evolved at the high tempera- 
ture to which the mineral was subjected in the experiment to 
determine the loss by calcination previously recorded. 

It may therefore be inferred, that the oxide of lead in Beu- 
dantite is combined with sulphuric acid. 

On the Triads made with Fifteen Things. 


If this inference be aclinittecl, it follows tliat the excess of 
sulphuric aciil beyond that required to saturate the oxide of 
leatl, is, tooether with the arsenic and phosphoric acids, com- 
bined with sesquioxide of iron, of which there is much more 
than sufiicient to neutralize those acids. The mineral may 
therefore be considered as a mixture of sulphate of lead, and of 
arseniate and sulphate of sesquioxideof iron with excessof base. 

The sulphate of lead cannot be regarded as in combination 
with the salts of iron, because no analogous combination is 
known. Nor is it more probable that arseniate and sulphate 
of sesquioxide of iron should exist in combination with each 
other. Hence the mineral would appear to be a simple mix- 
ture of three distinct salts. But it is crystallizeil ; and the 
crystalline form certainly is very similar to, if not identical 
with, that of cube-ore. Levy maintained that it was an ob- 
tuse rhombohedron with the vertical angle truncated. Descloi- 
zeaux, on the other hand, asserts that the crystals are cubes 
similar in all respects to those of cube-ore from Cornwall. 
{Ann. de Chim. et de Phjjs., vol. x, p. 77.) 

Professor Miller, howevei-, has not been able to obtain sa- 
tislactory measurements of the crystals. Now, as Beudantite 
contains in very sensible proportion the elements of cube-ore, — 
as the form of the crystals, to say the least, very nearly re- 
sembles that of cube-ore, — and as neither sulphate of lead nor 
sulphate of sesquioxide of iron forms crystals at all similar to 
those of cube-ore, the most probable conclusion seems to be 
that of Damour, namely, that Beudantite is nothing more than 
cid)e-ore containing an accidental mixture of much foreign matter. 
Such mixtures, as Damour observes, are frecjuentiy met with 
in the mineral kingdom, and present a very interesting subject 
of inquiry. An extended investigation to determine the 
amount of foreign matter which may enter into the composi- 
tion of crystals, and its power of distorting or modifying the 
crystalline form, would certainly yield many valuable results. 

XIX. On the Triads made "with Fifteen Things. 
By the Rev. Thomas P. Kirkman, M.A.^ 

THE neatest method of writing the solution of the problem 
mentioned at page 52 of this volume is the following: — 
























^3^ 1^2 












* Communicated by the Author. 

170 0)1 the Triads made laith Fifteen Things. 

The last three pairs of columns exhibit three systems of 
subinclices, which si/s(eins may be cyclically permuted, the 
letters remainincr uiulisturhed : this gives us two sets more 
each of six final columns, making three sets of six columns, 
any set of which being added to the primary column will solve 
the problem. If we now permute the letters abcde cyclically 
in these Gx3 cohunns, we shall obtain four times 6x3 co- 
lumns more, making 6x 14- columns in all, additional to the 
system of seven above written; so that we can complete the 
primary colunui into a solution in fiiteen ways, and this with- 
out repeating any triad : l)y this process we shall exhaust the 
45o triads that are possible with fiiteen things. All this I 
have long known ; but it never occurred to me to observe that 
the additional 6x 14 were exactly 12x7, and thus to make 
the pleasing variation, by which Mr. Sylvester has extended the 
puzzle over the remaining twelve weeks ot the quarter. We 
see that this is, as Mr. Cayley expected, a matter of cyclical 
permutation ; not of thirteen (a negative which he has proved), 
but of five letters. 

I obtained this property oi' the triads made with fifteen 
things four years ago, by observing that, if you substitute in 
Qi5, at page 195 of the second volume, N. S. of the Cambridge 
and Dul)lin Mathematical .Tournal, in the place of the small 
letters, the second instead of the first arrangement of Dg given 
on the preceding page, Q,^ can be broken up into seven co- 
lumns of five triads each, so as to solve this problem of the 
fifteen young ladies ; but Q,^, as it stands at page 195, cannot 
be so broken up. The solution of Mr. Cayley at page 52 
above is obtained by a like tentative process; and, in fact, 
all the solutions are of the same form, and can be made 
identical with the one above written, by disturbing the alpha- 
betical order, or that of the subindices in certain triads, or 
both, ill the first column. The question has yet to be mathe- 
matically treated: I do not feel satisfied with knowing how 
to form tliirty-five triads, which are found on trial, but not 
certainly proved before trial, to be capable of the required 
arrangement. We want to know, before trial, "iH'/it/ a school 
of fifteen can tlius be marched out till every pair have walked 
together, and why a school of twenty-one ca?i also, or cannot. 
I have a strong opinion, but will not undertake to prove the 
negative, that twenty-one cannot be thus arranged. 

Permit me, in conclusion, to enunciate the following pro- 
positions: — 

Theor. I. 5 x 3'"+' symbols can be arranged in ^(.5'3'"^' — 1) 
columns of triads, each column containing all tiie symbols, 
and so that every duad shall be once, and once only, employed. 

Theor. II. If r be any prime number, and otherwise not, 

On the Analysis of Waters hy the Soap- Test. 171 

r"*"*"^ symbols can be arranged in (;•'" + ' — 1) :(;•— 1) columns 
of r-plets, each column containinir all the symbols, and so 
that every duad shall be once, and once only, employed. 

Theor. III. li' r be any prime number, {}■- + ?•+ 1) symbols 
can be formed into {r' + r+ 1) r+ i-plets, so that every duad 
shall be once, and once only, employed. 

Theor. IV. If r be any prime number, and r^ + r+1 be 
prime, {n=) (r"- + r 4- ])(?'+ 1) symbols can be formed into 
71. n— I : r.r+ 1 r+ 1-plets, so that every duad shall be once, 
and only once, employed. 

Theor. V. Nine symbols can be arranged in seven sets each 
of four columns of triads, every column containing the nine 
symbols once, and so thai no triad shall be twice employed. 

Theor. VI. If R = A"B''C" ... L'lVr'N be any integer, of 
which A, B, C, ... L, M are prime factors in decreasing order, 
N being any number less than M, R symbols can be arranged 
in (A''-1):(A-1) columns of A-plets, + A".(B*-1):(B-1) 
columns of B-plets, + A^B'-lC^-l) : (C-1) columns of 
Cplets, + ... + A"B''C"... L'(M"^-1) : (M-1) columns of 
M-plets, +A"B'C"... L'M'" columns of N-plets, and this 
so that each column shall exhibit all ihe R symbols, and that 
every duad shall be once employed and repeated nowhere. 

Croft Rectory, near Warrington, 
August 6, 1850. 

XX. On the Action of the Soap-Test iqmn Water containing 
a Salt of Magnesia only, and lificwise upon Water containing 
a Salt of Magnesia and a Salt of Lime. By Dugald 
Campbell, F.C.S. London*. 

FOR some time back I have been engaged in analysing 
specimens of water-r-determining by actual experiment, 
besides the salts of the alkalies which they contain, the amount 
of phosphate of iron and salts of lime and magnesia in a gal- 
lon, testing them at the same time with reference to their de- 
grees of hardness, according to the plan adopted by Prof. 
Clark in the specification of a patent printed in the Reper- 
tory of Patent Inventions for 1841. 

When the quantities of phosphate of iron and salts of lime 
and magnesia found in a gallon of water were calculated each 
into its equivalent of chalk and added together, I had antici- 
pated that their amount would correspond, or nearly so, with 

* Communicated by the Author, having been read before the British 
Association, August 1850. 

172 Mr. D. Campbell un the Action of the Soap-Test 

the de;:;ree.s of hardness of the water as ascertained by the soap- 
test, this being the rule p;iven by Professor Clark in a private 
circular to his chemical friends to "infer tliede«irees of hard- 
ness hoin an ordinary analysis." But in this 1 was mistaken. 
1 therefore thouirht ii atlvisable to make some experiments 
with the soap-test upon water of which I knew the actual 

The soap-test I employed in the following experiments was 
prepared with the utmost care, the alcohol havin<r always been 
di<ijested with carbonate of potash ft)r many hours before being 
reduced to proof-spirit. The soap corresponded wiih 
Prof. Clark advises, nearly 1 oz. in a gallon of proof-spirit, 
giving a soap-test, thirty-two test measures of which formed a 
perfect lather with 100 like measmes of a standard solution 
of 16" hardness of lime, which remained all over the water for 
five minutes when first placed after shaking, and which could 
be renewed at any time by again agitating it. I'iie soap-test 
was likewise proved by standard solutions of lime of 12% 8°, 
G'^, 4°, 2= iiardness. 

The distilled water employed in making standard solutions 
was selected with much care, and tested in various ways to be 
sure of its purity. 

The first experiments which I made were upon water con- 
taining a salt of magnesia in different proportions. 

To prepare such solutions, 192 grains perfectly pure and 
dry sulphate of magnesia (MgO, SOg), which is the equiva- 
lent quantity of that salt to 16 grains carbonate of lime, were 
dissolved in a gallon of distilled water. This was considered 
as a standard of magnesia equal to 16° hardness of lime, or a 
standard of magnesia equal to 16". Fifteen other standard 
solutions were prepared from this, as follows: by taking one 
measure of the 16° standard, and adding fifteen like measures 
of distilled water to it, we have a standard of 1° magnesia; 
with two measures of original standard and fourteen like mea- 
sures of distilled water added to it, we have a standard of 2° 
magnesia; and so on up to 15°. 

The results which I obtained (see Table No. 1, p. 173) 
when treating these solutions with soap-test, were such as to 
intluce me to proceed with experiments upon mixed standard 
solutions of magnesia and lime. These I prepared as follows: — 
Magnesia standards ranjTinii from one to sixteen were made 


each to contain double the amount of the magnesian salt that 
the previous standards contained. Lime standards were then 
madeof3'2°, 24-°, 16°, 12°, 8% 4.° hardness in a gallon. When 
fifty measures of these lime standards were mixed with fifty 
like measures of the last magnesian standards, I then consi- 

upo7i Water containing a Salt of Magnesia. 173 

dered that I had standard solutions of 16°, 12% 8°, 6", 4°, 
2° hardness of lime, plus 1°, 2% 3" magnesia, and so on up 
to 1 6^ 

The Tables Nos. 2 to 7 give the number of soap-test mea- 
sures which I have found requisite to produce a perfect and 
renewable lather, when shaken with one hundred test mea- 
sures of these solutions in a phial capable of containing about 
five fluid ounces. 

Table No. 1. 

Table No. 2. 
















32 i 


+ 1° 

31 -6 





+ 2 




76 i 


+ 3 




9-6 I 


+ 4 




11-6 ': 


+ .'5 




136 1 


+ 6 






+ 7 






+ 8 






+ 9 






+ 10 






+ 11 



18 3 

24-9 ; 


+ 12 






+ 13 




28-5 ! 


+ 14 






+ 15 






+ 16 


Table No. 3. 

Table No. 4. 


















+ 1 



+ 2 



+ 2 



+ 3 



+ 3 



+ 4 



+ 4 



+ 5 



+ 5 



+ « 



+ 6 



+ 7 



+ 7 



+ 8 



+ 8 



+ 9 



+ 9 



+ 10 



+ 10 



+ 11 



+ 11 



+ 12 



+ 12 



+ 13 



+ 13 



+ 14 



+ 14 

14 3 


+ 15 



+ 15 



+ 16 



+ 16 


174 Mr. D. Campbell on the Action of the Soap-Test 
Table No. 5. Table No. 6. 




Soap-test ! Additional 



Soap-test Additional 




uieaMirc. "oap-tcst : 

ttaudard. 1 stimdard. 

measures, -^oup-tcst 




1 mc.isures. 

























14 6 

















+ 1-9 









15 4 

+ 40 

1 ^ 




+ 2-4 





+ 6-8 

1 6 



12 1 

-i- 121 , 
+ 12-7 





+ 110 









+ 15-2 





+ 135 





+ 18-7 





-1- 14-3 j 





+ 210 





+ 15-0 1 





+ 22 2 





+ 157 i 





+ 23-3 





+ 161 





+ 23-9 





+ 16-4 1 





+ 24-4 





+ 16-7 ' 





+ 250 


No. 7. 






Additional | 





measures. 1 
















1 2 




1 2 





























5 1 

i 2 























13-6 , 






15-2 1 




16 . 




Remarks upon the Tables. 

Table No. 1. Magnesia Standards. — On comparing the 
number of measures which I have found requisite 
to produce a perfect lather with the magnesia standards, with 
the number of soap-test measures which will cause a similar 
effect wiili the corresponding standards of lime*, it will be 

* These are the same which are given by Professor Clark in a private 
circular to his cheniiciil friends, and which I have introduced into Table 
No. 1, to serve for comparison with the results 1 have obtaiaed,;and which 
are detailed in that and the other tables. 

upon Water containing a Salt of Magnesia. 175 

seen tliat only as Hir as tlie 6tli degree do the magnesia cor- 
respond, or nearly so, witii the lime standards. And as the 
strength of the solutions increase, so much more do the dif- 
ferences increase, until a standard of 16^ magnesia, and a 
standard of 9' lime, leijuire nearly the same number of soap- 
test measures to produce a proper lather in each. 

Some experience is requisite in making experiments upon 
water containing magnesian salts alone, and likevvise upon 
matrnesian wat*. r mixed with lime salts. Ma«jnesian salts in 
water more or less produce a curd with soap which interferes 
in some measure with the lather. They likevvise do not act 
so readily upon soap as the salts of lime do ; so that in making 
an experiment, a good deal more agitation is recjuired to pro- 
duce a lather. 1 have found it best to add the soap-test little 
by little with agitation ; in fact, all solutions should be treated 
in the same manner as when a water of unknown hardness 
has to be tested. If the i-equisite quantity of soap-test be 
added at once to a standard, a good deal of shaking is required 
to produce even a curd: this is more the case as the quantity 
of magnesia increases, but by additional shaking the lather 
a{)pears. A proper lather once having been obtained, it 
can with very moderate shaking be restored again, not only 
for hours but for tiays afterwards, and improved as to sta- 
bility. The addition however of a little more soap-test with 
gentle agitation, instead of at once improving the lather, has 
the contrary effect, and a curd appears instead of the lather, 
or apparently the water is rendered hard, and it is only by 
very considerable agitation that the lather can be restored ; 
when restored, it is a better lather than before the addition of 
the last portion of soap-test : this operation may be repeated 
upon the same solution several times and with similar re- 
sults, by proceeding as above described, until a considerable 
amount of soap-test measures have been added above the 
quantity requisite to produce a proper lather. This is more 
particularly the case in the higher degrees. 

Table No. 2. 16° Lime plus Magnesia degrees. — On re- 
ferriuir to this table, it will be seen that the solution of 16*^ 
lime plus 1° magnesia, actually does not require so much 
soap-test to form a perfect lather as does the solution of 16° 
of lime alone, and as the magnesia increases in the solutions, 
the soap-test measures requisite to produce a lather diminish, 
until the solution of 16° lime plus 16° magnesia gives a lather 
with 27*9 measures, i. e. 4-* I soap-test measures less than is re- 
quired by the standard of lime of 16^ hardness. The action 
of a few more soap-test measures, when added to solutions in 
which a perfect lather had once been established, of appa-» 

176 Mr. D. Campbell on the Action of the Soap-Test 

rently rejuleriiifj them hard, was noticed in these as in the 
IbrmL^r solutions. 

Table No. 3. 12^ Lime plus Magnesia degrees. — It will he 
observed in this table that the magnesia acts similarly, althouoh 
scarcely so powerful as in the last experiments; but on the 
whole, the action of magnesia thoughout this series of expe- 
riments very much accords with its action in the former. 

Table No. 4-. 8° Lime plus Mag?iesia degrees. — On referring 
to this table, it will be seen that the magnesia acts upon the 
lime standard much as in the last experiments. 

Table No. 5. 6^ Lime plus Magnesia degrees. — On ex- 
amining this table, we find now that the magnesia begins to 
act differently towards the lime than it has hitherto done; 
the 6^ lime plus 1° magnesia is now equal in soap-test mea- 
sures to 6'' lime, at least the difference (0-2) may be considered 
within the limits of error of experiment; from 2' mag. up to 
6° there is a gradual rise, but at T'-" it begins to fall, and con- 
tiiujes to do so throughout the remaining solutions. I may 
remark that the latliers from 7' to 16° are not produced vviih 
the soap-test given in table, except with considerable agitation, 
and although thin, are perfectly free from curd and are re- 
producible at any future time by agitation. When a perfect 
lather has been produced by the minimum quantity of soap- 
test, the addition of a small (juantity more will reduce the 
lather to a curd; great agitation may jnoduce the lather 
again, and stronger than it was before the last addition of 
soap-test: if beyond a certain amount of soap-test has been 
added, a new action shows itself, which I have failed to notice 
in any of the previous solutions, which is, that shaking cannot 
restore the lather properly again until a certain amount of 
soap-test has been added; the additional quantities of soap- 
test I have had to add are in the table, and opposite the so- 
lutions in which I noticed this peculiarity; how to account 
for it I know not, and have not as yet had time to investigate 
into it. I am unable to account for the wide diff'erence in the 
amount of additional soap-tests between the numbers 7° and 8° ; 
as the other numbers seem to follow regularly, it may be owing 
to another point in some of these solutions at which much 
agitation and less soap-test would produce a lather, but which, 
although I have made many experiments, I have not succeeded 
in hitting upon. When to the lather established after the 
additional soap-tests a small quantity of soap-test is added, 
it renders it curdy, but shaking will re-establish the lather 

Table No. 6. 4° Lime "jcith Magnesia degrees. — On looking 
over this table, it will be noticed that the magnesia comes into 

upon Water cojitainiiig a Salt of Magnesia. 177 

action more fully, and for the first time the standard of lime 
with 1° magnesia requires more soap-test to form a lather 
than does the standard of lime alone; still it does not amcnnit 
to what wouki be necessary for 5^ lime. The soap-test mea- 
sures required to produce perfect laihers with 4% 5% 6^ and 
7°, are greater than was recjnired in the last series of expe- 
riments upon these numbers with the 6^ standard of lime. 
The same peculiarities of the soap-test upon some of these so- 
lutions were observed in this set of experiments as in the last. 
Table No. 7. ^2" Lime with Magnesia degrees. — On ex- 
amining this table, it will be seen ihat the solutions of this 
standard of lime with the first four magnesia degrees appear to 
require neaily as many soap-test measures as if thev were en- 
tirely lime standards. It will likewise be observed, on com- 
paring Table 4 with this table, that 7°, 8% 9^ magnesia with 8° 
lime, do not take each so many soap-test measures as 7"", 8"^, 9° 
magnesia with 2^ lime, to form proper laihers. Again, in Table 
No. 5, it will be seen tl)at each ot the magnesia degrees from 6'^ 
to IG'^, with the standard of lime which is 6^, do not take so 
many soap-tesi measures to form proper lathers, as do these 
magnesian solutions with 2° hardness of lime. On referring 
to Table 6, the same remark applies to these solutions as to 
the last, that is, that 2"' lime with each of the standards of 
magnesia from 6^ to 16^ require more soap-test to produce 
proper lathers than solutions of 4° lime with each of these 
magnesian standards require. I would call attention again 
to Table 7, to notice a rapid descent in soap-test mea- 
sures between 10^ and 11° magnesia; I have made many ex- 
periments if possible to explain this, but without success. I 
can only observe, that in certain stages of a series of expe- 
riments of a standard of lime with magnesia, it requii'es much 
care, attention and observation, to mark when the lathv.^" pre- 
vails over the curd, and to, obtain at this particular stage uni- 
form lathers, more especially when the soap inclines to form 
a curd in a solution, together with a lather, at the same time. 
If tiiese points are not attended to, and no perseverance em- 
ployed in agitating the solutions, uniform results cannot be 
exj)ected. The other observations I have made on the pre- 
ceding series of waters are applicable to these. The inferences 
which I draw from the foregoing experiments are as follows : — 
1st. That water containing sulphate of magnesia alone acts 
towards the soap-test in producing with it a perfect lather, 
similarly or nearly so, as does water containing a lime salt 
alone, but only when the equivalent of magnesia salt does not 
exceed 6 grs. of carbonate (.f lime in a gallon of water. 

2nd. That the degrees of hardness of an ordinary water 
P/iil. Mag. S. 3. Vol. 37. No, 249. Sept. 1850. N 

1 78 On a ncxo Accelerating Process in Photography. 

cannot be inferred by the rnle : — Compute the grains of lime, 
magnesia, oxides of iron, ahnnina, in a gallon of water, each 
into its ecjuivalent ol chalk: the sum of these equivalents will 
be the hardness of the water. 

3rd. That the degrees of hardness of a water containing 
magnesia and lime salts, as shown by the soap-test as it is now 
applieil, cannot in almost every case be taken as representing 
the amount of these salts in the water; nor in nearly every 
instance can it be considered as yfiving the amount of lime in 
a water when magnesia is present. 

4th. That water might show by the soap-test a small de- 
gree of hardness in comparison to the considerable quantities 
of salts of magnesia and ol lime it might contain, and trusting 
to this method of analysis alone when selecting water lor 
ordinary use and for steam purposes, might lead to a water 
being selected which might not be conducive to the general 
health, and wliich would leave considerable deposit in vessels 
in which it was boiled, — a great deterioration to its use in 
steam generating. 

XXI. On an Accelerating Process in Photography, 
By J. MiDDLETON, F.G.S."^ 

THE following method of prepaiing sensitive paper, may, 
perhaps, be welcome to photographers on account of the 
great sensibility which it confers; it has the additional recom- 
mendation, moreover, of being very simple and constant in its 

I beat up albumen of the egg of the duck till it becomes 
liquid, and then mix it with water in the proportion of eighty 
xTvains of the former to an ounce of the latter. I add to this 
solution iodiile of potassium in the proportion of twenty-five 
grains to the ounce. Prior to the application of this solution 
1 wash the size from the side to be rendered sensitive, by 
means of a camel-hair brush, and when dry I float the paper 
on the solution, for from three to four minutes, and when 
drained and dried I lay it aside for use. 

When about to be used for taking a picture, the paper, 
prepared as above directed, is to be washed with aceto-nitrale 
of silver, in the proportion of sixty grains of nitrate and 
eighty grains of acetic acid to an ounce of water (Talbot's 
strength). I apply the solution widi a glass rod, in the 
manner recommended some time since by a writer in the 
Philosophical Magazine, using about forty grains of it to a 

* Communicated by the Author. 

Mr. R. Crossley on Algcritef a new Mineral Species. 179 

quarto pafje, and allow the paper to dry in the dark ; it is now 
ready lor the camera. While applying the sensitive coat, as 
also while bringing out the })icture, I take the precaution to 
use a yellow light. I find that from ten to fifteen seconds is, 
with ordinary smi-light, sufiicient exposure, the latter being 
generally too great. 

When the picture has been taken no trace of it appears on 
the paper, but it comes speedily out on the application of a 
saturated solution of gallic acid. I turn up the edges of 
my paper and [TX)ur the solution on till the paper is entirely 
covered, and keep it so till the picture has come sufficiently 
out, when I fix it in the usual way. 

I find that if bromide of potassium be substituted for iodide 
of potassium, in the first process, a picture is obtained; but 
the time of exposure required is then about a minute. Again, 
bromide or chloride of potassium does not serve to accelerate, 
as in the ordinary processes, but the contrary; gallic acid too, 
added to the aceto-nitrate, destroys sensitiveness. I find also, 
that if the albumen be dried, and afterwards dissolved up 
and used as above described, it has lost its photographic 
value; a circumstance, which would seem to indicate that 
photographic properties are connected with or dependent 
upon molecular arran,o;ement. 

The employment of albumen in photography is not, I be- 
lieve, new: it has not, however, so far as 1 am aware, been 
used in the way or with the eflfect stated above. 
Agra, 18th June, 1850. 

XXII. Alger ite, a new Mineral Species. 
Bi/ Richard Crossley, Esq.^ 

A DETAILED description of this mineral by Mr. F. 
Alger, accompanied with an analysis by Mr. T. 8. Hunt, 
was published in the American Journal of Science for July 
1849, vol. viii. I have since, at the request of Mr. Alger, 
made a re-examination. The results obtained vary but little 
from those of Mr. Hunt, though this variation is essential to 
the formula. Algerite, named by Mr. Hunt in honour of its 
discoverer, Mr. Alger, is found in the town of Franklin, 
Sussex County, New Jersey. It is sparingly disseminated in 
prismatic crystals through a bed of pure crystalline limestone. 
The crystals when undecomposed are of a honey-yellow colour, 
and more or less penetrated by the matrix : some are conta- 
minated by graphite, and othei's are encrusted with idocrase, 

* Communicated by \V. G. Lettsom, Esq, 


l!sO Mr. 1\. Crosbley on Algerite, a nexv Mineral Species. 

whicli mineral also occurs at lliis locality. The honey-yellow 
crystals <i;ive a spec. grav. 2*78. Hardness from 3 to y-5. 
Brittle, siibtranslucent. Before the blowpipe alone it fuses 
readily to a white blebhy jilass. With soda it fuses to a dirty 
white s'.aijj. With borax and phosphorus salt it «^ives a bead, 
faintly tinged by iron, encUvsinfr a siliceous skeleton. Heated 
in a closed tube it gives off' water which reacts feebly alkaline, 
and the powder changes in colour I'rom light buff" to light 
brown. It is perfectly attackable by a mixture of sulphuric 
and hydrochloric acids. 

Crystals of the mineral, carefully cleaned, gave for its com- 
position — 

Silica 49-96 

Alumina 24*41 

Peroxide of iron . . . 1'48 

Magnesia 5*18 

Carbonate of lime . . 421 

Potash 9-97 

Water 506 


The amount of carbonic acid directly determined is equal 
to that in the carbonate of lime obtained. It is therefore evi- 
dent that the lime is not a constituent of the mineral. 

DeductinfT the carbonate of lime, and calculating the re- 
maining members for per-centage proportions, we shall have 
for the composition of Algerite, — 

Silica .52-00 

Alumina .... 
Peroxide of iron 
Magnesia .... 



100 00 

The above composition is very well represented by the 

3(A12 03, 2Si03) + (MgO, KO)3Si03 + 3HO; 

and there being no previously known mincn'al which gives the 
above characters, composition and formula, Algeiite must ne- 
cessarily rank as a new species. 
Boston, Mass. U.S., April 29, 1850. 


of oxygen. 














10 38 




[ 181 ] 

XXIII. On the Di fusion of Liquids. 
By Thomas Graham, F.R.S.^ F.C.S."^ 

ANY saline or other soluble substance, once liquefied and 
in a state of solution, is evidently spread or diffused 
uniformly through the mass of the solvent by a spontaneous 

It has often been asked whether this process is of the nature 
of the diffusion of gases, but no satisfactory answer to the 
question appears to be obtained, owing, I believe, to the sub- 
ject having been studied chiefly in the operations of endos- 
mose, where the action of diffusion is complicated asul obscured 
by the imbibing power of the membrane, which is peculiar 
lor each soluble substance, but no way connected with the 
diffusibility of the substance in water. Hence also it was not 
the diffusion of the salt, but rather the diffusion of the solution, 
which was generally regarded. A difi'usibility like that of 
gases, if it exists in liquids, should afford means for the sepa- 
ration and decomposition even of unequally diffusible sub- 
stances, and being of a purely physical character, the neces- 
sary consequence and index of den si hj, shoulti present a scale 
of densities for substances in the state of solution, analogous 
to vapour densities, which would be new to molecular theory. 

M. Gay-Lussac proceeds upon the assumed analogy of 
liquid to gaseous diffusion in the remarkable explanation 
which he suggests of the cold produced on diluting certain 
saline solutions, namely, that the molecules of the salt expand 
into the water like a compressed gas admitted into additional 

The phsenomena of solubility are at the same time con- 
sidered by that acute philosopher as radically different from 
those of chemical affinity, and as the result of an attraction 
which is of a physical or mechanical kind. The characters 
indeed of these two attractions are strongly contrasted. Che- 
mical combination is uniformly attended with the evolution of 
heat, while solution is marked with equal constancy by the 
production of cold. The substances vvliich combine chemically 
are the dissimilar, while the soluble substance and its solvent 
are the like or analogous in composition and properties. 

In the consideration of solubility, attention is generally en- 
grossed entirely by the quantity of salt dissolved. But it is 
necessary to apprehend clearly another character of solution, 
namely, the degree of force with which the salt is held in so- 
lution, or the intensity of the solvent attraction, (juite irre- 

* From tlie Philosophical Transactions for 1850, part i.; having been 
received by the Rojal Society November 16, and read December 20, 1849. 

182 Prof. Graham on the Diffusion of Liquids. 

spective of qiinntity dissolved. In the two solid crystalline 
hytliates, pyioiihospliate of soda and sulphate of soda, we see 
tile same ti-n e(]uivalents of water associated with both salts, 
but obviously united with unecjual defrrees of force, the one 
hydrate bein<r persistent in dry air anil the other liighly efflo- 
rescent. So also in the solutions of two salts which are equally 
solul)le in point of quantity, the intensity of the attraction 
between the salt and the water may be very different, as ex- 
emplilied in the large but feeble solubility in water of vSuch 
bodies as the iodide of starch or the sulphindylate of potash, 
compared with the solubility of hydrochloric acid or of the 
acetate of potash, which last two substances are capable of 
precipitating the two former, by displacing them in solution. 
Witness also the unequal action of animal charcoal in with- 
drawing different salts irom solution, although the salts are 
equally soluble; and the unequal effect upon the boiling-po': t 
of water produced by dissolving in it the same weight of- i- 
rious salts. Besides being said to be small or great, the s( u- 
bility of a substance has also therefore to be described as \\ ( ak 
or strong. 

The gradations of intensity observed in the solvent force 
are particularl}' referred to, because the inquiry may arise 
how far these gradations are dependent upon unequal diff^usi- 
biliiy ; whether indeed rapidity of diff"usion is not a measure 
of tlie force in question. 

I have only further to premise, that two views may be taken 
of the physical agency i)y which gaseous diff'usion itself is 
effected, which are equally tenable, being both entirely suffi- 
cient to explain the phsenomena. 

On one theory, that of Dr. Dalton, the diffusibility of a gas 
is referred immediately to its elasticity. The same spring or 
self-repulsion of its particles which sends a gas into a vacuum, 
is supposed to propel it through and among the particles of 
a different gas. 

The existence of an attraction of the particles of one gas 
for the particles of all other gases is assumed in the other 
theory. This attraction does not occasion any diminution of 
volume of gases on mixing, because it is an attraction residing 
on the surfaces of the gaseous molecules. It is of the same 
intensity for all gases, hence its effect in bringing about inter- 
mixture is dependent upon the weight of the molecules of the 
gases to be moved by it; and the velocity of iliffusion of a gas 
comes to have the same relation to its density on this hypo- 
thesis as upon the other*. 

* Both of the molecular theories of the diffusion of gases were first pub- 
licly explained, and at the same time ably discussed, with the reference to 

Prof. Graham on the Diffusion of Liquids. 183 

The surface attraction of molecules assumed will recall the 
surface attraction of liquids, which is found necessary to ac- 
count for the elevation of liquids in tubes and other phaeno- 
mena of capillary attraction. 

(1.) An early preliminary experiment was made upon the 
licjuid diffusion of a body, with whose diffusion as a f^as we 
are already well acquainted, namely, carbonic acid dissolved 
in water. 

Two half-pound stoppered glass bottles were selected, of 
which the mouths were 1*2 inch in diameter, and the lips were 
ground flat so as to close tight when applied together (fig. 1). 
One of them, placed firmly in an Fig. 1. 

upright position, was filled to the 
base of the neck with carbonic acid 
water. Over this distilled water 
was poured, care being taken to 

disturb the liquid below as little as 

possible, in filling up the neck. The 
second bottle, filled with distilled 
water and inverted upon a glass 
plate, was slipped over the first at 
the water-trough. The solution of 
carbonic acid in the lower bottle 
was thus placed in free communica- 
tion by an apertureof 1*2 inch, with 
anequal volume of pure water in the 
upper bottle. It was expected that the carbonic acid would 
be found, in time, equally diffused through both bottles. 

After forty-eight hours, the upper inverted bottle was again 
slipped off from the lower one, upon a glass plate, and the 
ratio of the gas found in the upper to that in the lower bottle 
determined by the weight of carbonate of baryta which the 
liquids of the two bottles afforded respectively. It was as 
ri8 to 12-80 (about 1 to 11), instead ot the ratio of e(]uality, 
which would undoubtedly be the ultimate result of difi^usion, 
were sufficient time allowed. 

After five days, in a second experiment with a weaker solu- 
tion of carbonic acid, the gas was found to be distributed — 
In upper bottle . . . 1*63 
In lower bottle .... 8*44' 
or in the proportion of 1 to 5 nearly. 

the law of diffusion which had been drawn from observation, by my late 
friend Mr. T. S. Thomson of Clitheroe. A decided preference was given 
by Mr. Thomson, and also by the late Mr. Ivory, to the last, or the attrac- 
tion tlieory of diffusion, over that of gases being vacua to each other. See 
Phil. Mag., 3rd series, vol. xxv. pp. 51, 282. 

18* Prof. Graliam on the Di/fiision of Liquids. 

In other experiments where tlie liquid in the upper bottle 
was a solution in water ot nitrous oxide ^as, instead of pure 
water, the carbonic acid of the lower bottle was also observed 
to dilluse into the licjuid above it, as ireely as it did into pure 
water in a comparative experiment; the ultimate ratios being 
1 to 0'12 in the nitrous oxide li(jui(l, and 1 to 0* 10 in the water 

With the necks of the pair of bottles t)ccupied by sponge 
charged with distilled water, the ditt'usion of the carbonic acid 
of the lower bottle proceeded with little change in its rapidity, 
or in the result when nitrous oxide was placed above it. The 
carbonic acid found in the upper bottle, and which had dif- 
fused into it from the lower, was 0*231 when the upper bottle 
contained water alone, and 0*229 when it was water charged 
with three-fourths of its volume of nitrous oxide gas, — to 1 
carbonic acid remaining undiftused in the lower bottle in both 

It appeared, then, that the liquid diffusion of carbonic acid 
was a slow process compared with its gaseous diffusion, quite 
as much as days are to minutes. 

That this diffusion of the li(|uid carbonic acid takes place 
with undiminished vigour into water already saturated with 
nitrous oxide, tiie substance of all others most resembling 
carbonic acid in sohibiiity and the whole range of its physical 
qualities. The diffusion of the liquid carbonic acid appears 
no more repressed by the liquid nitrous oxide, than the diffu- 
sion of gaseous carbonic acid is by gaseous nitrous oxide. 

But the chief interest of these observations was the practical 
solution which they give to the question, whether, in conduct- 
ing experiments on liquid diffusion, accidental causes of dis- 
turbance and intermixture of two liquids, communicating 
freely with each other, can be avoided. It was made evident 
that little is to be feared from accidental dispersion when or- 
dinarv precautions are taken. 

An excess of liensity in the lower liquid of not more than 
__i_-_th part is found adecpiate to prevent any onsiderable 
change of place of the latter, — from expansion by heat, acci- 
dental tremors and such distmbing causes, which must exist, 
— for days together. 

(2.) Another early inquiry was, how far is the diffusion of 
various salts governed or modified by the density of their so- 

Solutions ofeigiit hydrated acids and salts were prepared, 
having the comnion tlensity of 1*200, and were set to diffuse 
into water in the following njanner: — 

Eighteen or twenty six-ounce phials were made use of to 

Prof. Graham on the Division of Liquids. 185 

contain tlie solutions, and to form what I shall call the Solu- 
tion phials or cells. They were of the same make and selected 
from a large stock, of the common aperture of I '175 inch. 
Both the mouths and bottoms of these phials were ground 
flat. The mode of making an experiment was first to fill the 
phial to the base of the neck, or rather to a constant distance 
of 0-G inch below the ground surface of the lip. A little disc 
of cork, provided with a slight upright peg of wood, was tiien 
floated upon the solution in the neck, after having been first 
dipt in water. The neck itself was now filled up with pure 
water by means oi'a pointed sponge, the drop suspended from 
the sponge being made to touch the peg of the float, and water 
caused to flow in the gentlest manner, l)y sligluly pressing the 
sponge. The only other part of the apparatus, the water-jar, 
was a plain cylindrical glass jar, of which the inner surface of 
the bottom was flat or slightly concave, to give a firm support 
to the phial. The phial, with its solution only, was first 
placed in this jar partly filled with distilled water, and the 
neck of the former was then filled up with distilled water in 
this position, as before described, to avoid any subsequent 
movement. The phial was ultimately entirely covered to the 
depth of an inch with water, which required about 30 ounces 
of the latter, fig. 2. The saline solution in Fiir. 2. 

the diffusion cell or phial thus communicated c^^:;;^ 
freely with about five times its volume of pure '— " 
water, the liquid atmosphere which invites 
diff'usion. Another modification of this pro- 
cedure was the substitution of phials cast in 
a mould, of the capacity of 4 ounces, or more 
nearly 2080 grs., which were ground down 

to a uniform hei<xht of 3'8 inches. The neck 

® . ... 

was I '25 inch in diameter and 0*5 mch in 

depth ; and the phial was filled up with the 


solution to be difl'used to that point. The solution cell or 
phial and the water-jar form together a diffusion cell. 

The diff'usion was stopt, after twenty-seven days in the pre- 
sent experiments, by closing the mouth of the phial with a 
plate of glass, and then raising it out of the water-jar. The 
quantity of salt or of acid which had found its way into the 
water-jar, — the diffusion product as it may be called, — was then- 
determined by evaporating to dryness for the salts, and by 
neutralizing the same liquid with a normal alkaline solution 
for the acids. The quantities of the acids diffused are esti- 
mated at present as protohydrates for the sake of comparison 
with the salts. 


Prof. Grnliam on the Diffusion of Liquids. 

Table I. — DilFusion of Solutions of Density 1*200. Temp. 
66° Fahr. 

Placed in solution cell. Foutid in water-jar < 

Proportion of anhy- 
drous salt, or of acid Boiling- 
protohydratc, to 100| point, 
of water. 

In grains. Ratio. 

Diffusion product. 

Chloride of sodium 

Nitiic acid 

Sid pli uric acid 

Clilorideof|)otassiuin(deusity ri78) 

Bi>ulphate of potash 

Nitrat • of soda 

Sulphate of magnesia 

Sulphate of copper 

34 86 









95 87 


215 42 

168 68 






It Appears that tlie diflfusion from solutions of the same den- 
sity is not equal but liitrhiy variable, raniriiig from 1 toO'1333. 

The results also favour the existence of a relation between 
large or rapid diffusibility and a high boiling-point. The latter 
property may be taken to indicate of itself a higli degree of 
attraction between the salt and water. 

I. Characters of Liquid Diffusion. 

1. Diffusion of Chloride of Sodium. 

The characters of liquid diffusion were first examined in 
detail in the case of this salt. 

(1.) Do different proportions of chloride of sodium in solu- 
tion give corresponding amounts of diffusion? 

kSolutions were prepared of chloride of sodium in the pro- 
portion of 100 water with I, 2, 3 and 4 parts of the salt. 

The diffusion of all the solutions was continued for the same 
time, eight days, at the mean temperature of 52°*5 Fahr. 

Proportion of salt to 100 water. 

Diffusion product. 

In grains. Ratio. 


2-78 1- 
554 1-99 
8-37 3-01 
11-11 4-00 

The quantities diffused appear therefore to be closely in 
proportion (for this salt) to the quantity of salt in the diffusing 
solution. The density of the solutions containing 1, 2, 3 and 
4 parts of chloride of sodium, was at 60^, 1-0067, 1*0142, 

Prof, Graham on the Diffusion of Liquids. 187 

1*0213, 1"0285. The increase of density corresponds very 
nearly with the proportion of chloride of sodium in solution. 
A close approach to this direct relation is indeed observable 
in most salts, when dissolved in proportions not exceeding 4 
or 5 per cent. 

The relation which appears in these results is also favour- 
able to the accuracy of the method of experimenting pursued. 
The variation from tiie speculative result does not in any ob- 
servation exceed 1 per cent. 

(2.) Is the quantity of salt diffused affected by temperature? 

The diffusion of similar solutions of chloride of sodium was 
repeated at two new temperatures, 39^'6 and 67°, the one 
being above and the other below the preceding temperature. 
It was necessary to use artificial means to obtain the low tem- 
perature owing to the period o'i the season. A close box of 
double walls, namely the ice-safe of the Wenham Ice Com- 
pany, was employed, masses of ice being laid on the floor of 
the box, and the water-jars supported on a shelf above. The 
water and solution were first cooled separately for twenty- 
four hours in the ice-box, before the diffusion was commenced. 
It was found that the temperature could be maintained within 
a range of 2° or 3° for eight days. It was doubtful however 
whether the temperature was constantly the same to a degree 
or two in all the jars; and the results obtained at an artificial 
temperature were always less concordant and sensibly inferior 
in precision to observations made at the atmospheric tempe- 

Diffusion of Chloride of Sodium. 

Proportion of salt to 100 water. 

DiflFusion product. 

In grains. Ratio. 

1 At 39?-6 

2 At 39°-6 

3 At 39°-6 

4 At 39°-6 

1 At 67° 

2 At 67° 

3 At 67° 

4 At 67° 















The proportionality in the diffusion is slill well-preserved 
at the different temperatures. The deviations are indeed little, 
if at all, greater than might be occasioned by errors of obser- 
vation. The ratio of diffusion, for instance, from the solutions 
containing 4 parts of salt, is 3"80 and 3*89 for the two tem- 
peratures, which numbers fall little short of 4. 

The diffusion manifestly increases with the temperature, 

188 Prof. Graham on the Diffusion of Liquids. 

and as far as can be determined by three observations, in 
(hrect proportion to the temperature. Tlie diffusion-product 
from the 4 per cent, solution increases from 10 grs. to 13*60, 
with a rise of temperature of 27^'4', or rather more tlian one- 
third. 8up})osiii<r the same progression continued, the diffu- 
sibiiity of chloride of sodium would be doubled by a rise of 
81' or 85 degrees. 

(3.) The progress of the diffusion of chloride of sodium in 
such experiments as have been narrated, was further studied 
by intercepting the operation alter it had proceeded for dif- 
ferent periods of 2, 4, 6 and 8 days. Tlie solution employed 
was that containing 4 parts of salt to 100 water. Two of the 
six-ounce phials were diffused at the same time for each 
period. The temperature given is the mean of the tempera- 
tures of a water-jar observed each day of the period. The 
daily fluctuation was not more than two or three-tenths of a 
degree Fahr. 

In 2 days, temperature 63^*7; the salt diffused was 4*04 
and 'i'SG grs. ; mean 3*95 grs. 

In 4 days, temperature 63°'7 ; the salt diffused was 6*78 
and 7*12 grs. ; mean 6*95 grs. 

In 6 days, temperature 63'^'8 ; the salt diffused was 10*02 
and 9*70 grs. ; mean 9*86 grs. 

In 8 days, temperature 64°; the salt diffused was 13*00 and 
13*25 grs.; mean 13*12 grs. 

The proportion diffused in the first period of two days is 
given directly in the first experiments. The proper diffusion 
for each of the three latter periods of two days is obtained by 
deducting from the result of each period the result of the 
period which precedes it : — 

Diffused in 1st two days . . 3*95 grs. 

Diffused in 2nd two days . . 3*00 grs. 

Diffused in 3rd two days . . 2*91 grs. 

Diffused in 4th two days . . 3*26 grs. 

The diffusion appears to proceed pretty uniformly, if the 
amount diffused in the first period of two days be excepted. 
Each of the phials contained at first about 108 grs. of salt, of 
which the maximum quantity diffused is 13*12 grs. in eight 
days, or ^ of the whole salt. Still the diffusion must neces- 
sarily follow a diminishing progression, which would be 
brought out by continuing the process for longer time, and 
appear at the earliest period in the salt of most rapid diffusion. 

All the experiments which follow being made like the pre- 
ceding on comparatively large volumes of solution in the phial, 
and for ecjually short periods of seven or eight days, may be 
looked upon as exhibitingpretty accurately the initial diffusion 

Prof. Graham on the Dijfusion of Liquids. 189 

of such solutions, the influence of the cliniinisliinf(prof>re';sion 
beinjT still small. The volume of water in the water-iar is 
also relatively so large, that the experiment approaches to the 
condition of diffusion into an Unlimited Atmosphere. 

2. Diffusion of various Salts and other Substances. 

With these notions regarding the influence of temperature 
and proportion of salt on the amount of tliff'usion, an exami- 
nation was next undertaken of the relative diflusibility of a 
variety of salts and other substances. The results of this first 
survey I shall state as shortly as possible, as I consider these, 
as well as the experiments which preceded, as of a preliminary 
character. The experiments were all made by means of the 
diffusion phials already described, namely, the six-ounce 
phials, and with similar manipulations. 

In the following experiments, the diffusion took place at a 
temperature ranging from 62° to .59°, mean 60°-5, and was 
continued for a period of eight days; the proportion of salt in 
solution to be diffused being always 20 salt to 100 water, or 5. I add as usual the density of the solutions. 

Table II. — Diffusion of solutions of 20 salt to 100 water, at 
60°-5, for eight days. 

Name of salt. 

Density of 
solution at 60°. 

Anhydrous salt diffused. 

In grains. 


Chloride of sodium ... 



Chloride of sodium ... 




Sulphate of magnesia... 




Nitrate of soda 





Nitrate of soda 

Sidphate of water 

Sulphate of water 




Crystallized cane-sugar 




Fused cane-sugar 

, 1-066 



Starch-sugar (glucose) 

' 1-061 



Treacle of cane-sugar 

! 1-069 


] 32-55 









The following additional ratios of diffusion were obtained 
from similar solutions at a somewhat lower temperature, 
namely 48°; — chloride of sodium 100, hydrate of potash 
15 r93, ammonia (from a 10 per cent, solution, saturated with 
chloride of sodium to increase its density) 70, alcohol (satu- 
rated with chloride of sodium) 75-74, chloride of calcium 
71-23, acetate of lead 4-5-46. 

1 90 Prof. Graham o)i the Diffusion of Liquids. 

\Miere two experiments upon tlie same salt are recorded 
in ilie table they are seen to correspontl to wiiliin 1 part in 
4 0, which may be considered as the limit of error in the pre- 
sent observations. It will be reniarked thnt the diffusion of 
cane- and starch-sugar is sensibly e()ual, and double that of 
i2[iini-arabic. On the oiher hand, the sugars have less than 
liaif llie diff'usibility of cidoride of sodium. It is remarkable 
that the sj)eci(ically lightest and densest solutions, those of the 
sugars and of sulphate of magnesia, aj)proach each otiier 
closely in diff'usibility. On comparing together, however, two 
substances of similar constitution, such as the two salts, chlo- 
ride of sodium anrl sulphate of magnesia, that salt appears to 
be least diffusive of which the solution is densest. 

But the most remarkable result is the diffusion of albumen, 
which is low out of all proportion when compared with saline 
bodies. The solution en)ployed was the albumen of the egg, 
without dilution, but strained through calico and deprived of 
all vesicular matter. As this liquid, with a density of l-Oil, 
contained only l^-oy parts of dry matter to 100 of water, the 
proportion diffused is increased in the table to that for 20 
parts, to correspontl with the other substances. In its natural 
alkaline state the albumen is least iliffusive ; but when neutral- 
ized by acetic acid, a slight precipitation takes place and the 
li(]uid filters more easily. The albumen is now sensibly more 
diffusive than before. Chloride of sodium appears 20 times 
more diffusible than albumen in the table, but the disparity is 
really greater ; for nearly one-half of the matter which diff'used 
consisted of inorganic salts. Indeed the experiment appears to 
promise a delicate method of proximate analysis peculiarly 
adapted for animal fluids. The value of this low diff'usibility 
hi retaining the serous or albuminous fluids within the blood- 
vessels at once sugjiests itself. 

or) f 

Similar results were obtained with egg albumen diluted and 
well-beaten with 1 and 2 volumes of water. The solution 
diluted with an equal bulk of water, and made slightly acid 
with acetic acid, contained 7| dry matter to 100 water. Dif- 
fused from two four-ounce bottles of 1*25 inch aperture, for 
seven days, at a mean temperature of 43°'5 F., it gave pro- 
ducts of 1*73 and 1*48 gr., from the evaporation of two water- 
jars, in which cubic crystals of common salt were abundant. 
The whole matter thus diffused in two cells was found to con- 
sist of — 

Coagulable albumen . . 0"94 gr. 

Soluble salts 227 grs. 

3-21 grs. 

The diffusion product of the same solution of albumen left 
alkaline, or without the addition of acetic acid, in the same 

Prof. Graham 07i the Diffusion of Liquids. 191 

circumstances, was Tl-l and 1*20 grs. in two cells; and con- 
sisted of — 

CoafTiiJable albumen . . 0*63 gr. 

Soluble salts 1^ gr. 

2-61 grs. 

The diffusion product of a solution of 7^ parts of chloride 
of sodium to 100 water, from similar cells and for the same 
time and temperature, would amount to about 30 grs, of salt. 
It is to be remarked also that 5'5S grs. of the ignited salt dif- 
fused from albumen contained 1-32 gr. of })otash or 23-9 per 
cent., which is a high proportion, and indicates that salts of 
potash diffuse out more freely from albumen than salts of soda. 

Nor does albumen impair the diffusion of salts dissolved 
together with it in the same solution, although the licjuid re- 
tains ils viscosity. Three other substances, added sejiarately 
in the projiortion 5 parts to 100 of the undiluted solution of 
egg albumen, were found to diffuse out quite as freely from 
that liquid as they did from an equal volume of pure water: 
these were chloride of sodium, urea and sugar. Urea proved a highly diffusible substance. It nearly coincided in 
rate with chloriile of sodium. 

A second series of salts were diffused containing 1 part of 
salt to 10 of water; a smaller proportion of salt which atlmits 
of the comparison of a greater variety of salts. The tempe- 
rature during the period of eight days was remarkably uni- 
form, 60°— 59°. 

Table III. — Diffusion of solutions of 10 salt to 100 water 

at 59°-5. 

Density of 

Anhydrous salt diffused. 

Name of salt. solution at 60^ 

In grains. Means. 

Chloride of sodium 

Chloride of sodium 

Nitrate of soda 

1-0668 1 32-3 1 

1-0668 1 32-2 32-25 

1-0622 30-7 30-7 

Cliloride of potassium 
Chloride of ammonium 

Nitrate of potash 

Nitrate of potash 

Nitrate of ammonia ... 
Iodide of potassium ... 
Chloride of barium ... 

Sulphate of water 

Sulphate of water 

Sulphate of magnesia... 
Sulphate of magnesia... 
Sulphate of zinc 




40 20 

















Sulphate of zinc 

192 Prof. Graham an the Diffusion of Liquids. 

Before adverting: to the rehuions hi diffusihiUty wliich ap- 
pear to exist between certain saUs in the preceding table, 1 
may state »he resuks of the chllusion of the same solutions at 
a lower temperature. 

Table IV. — Dillusion of solutions of 10 salt to 100 water 
at 37°-5. 

Name of salt. 

Anhydi-ous salt ditfiised. 

In grains. Means. 

Chloride of sodium 


Chloride of sodium 

22-74 22-47 

Nitrate of soda 

Nitrate of soda 

i.^3-05 22-79 
31-14 31-14 

Chloride of ammonium 

Nitrate of potash 

Nitrate of potash 

Nitrate of ammonia 

28-84 , 

28-56 28'70 
29-19 ; 29-19 
28-10 28-JO 

Iodide of potassium 

Chloride of barium 

21*42 j 21-42 

Sulphate of water 


Sulphate of water 

28-60 29-85 

Sulphate of magnesia 


Sulphate of magnesia 

13-11 13-07 

Sulphate of zinc 


Sulphate of zinc 

13-33 12-60 

The near equality of the quantities diffused of certain isc- 
morphous salts is striking at both temperatures. Chloride of 
potassium and chloride of ammonium give 40°-15 and 40°-20 
grs. respectively in the first table. Nitrate of potash and ni- 
trate of ammonia 355.5 (mean) and 35°-3 grs. respectively in 
the first table, and 28-70 and 29-19 grs, in the second table. 
Sulphate of magnesia and sulphate of zinc 15*45 and 15*8 grs. 
(means) in the first table, with 13-07 and 12 60 grs. in the 
second. The relation observe<l is the more remarKable, that it 
is that of equal weights of the salts diffused, and not of atomi- 
cally equivalent weights. In the salts of ammonia and potash, 
this equality of diffusion is exhibited also, notwithstanding con- 
siderable differences in density between their solutions ; the 
density of the solution of chloride of ammonium, lor instance, 
being 1-0280 and that of chloride of potassium 1-0596. It 
may have some relation however, but not a simple one, to the 
density of the solutions; sulphate of magnesia, of which the 
solution is most dense, being most slowly diffusive; and salts 
of soda being slower, as they are generally denser in solution, 
than the corresponding salts of potash. Nor does it depend 

Prof. Graham on the Diffusion of Liquids, 193 

upon equal solubility, for in none of the pairs is there any ap- 
proach to equality in that respect. 

A comparison was now made of the diffusibility of several 
acids. They were diffused from the same six-ounce phials, 
and for eight days. Solutions were prepared in the proportion 
of 4 parts of the anhydious acid to 100 ))arts of water. The 
quantity of acid which diffused into the water-jar was estimated 
by the proportion of carbonate of soda which it neutralized. 

Table V. — Diftlision of acid solutions (1- acid to 100 water) 

at 59°'3. 

Name of acid. 

Density of 
solution at 6u°. 

Anhydrous acid diffused. 

In grains. Means. 

Nitric acid 

10243 29-21 


10225 34-22 


Hydrochloric acid 

Sulphuric acid 

{ 33-99 ; 341 
10317 ' 18-71 

Acetic acid 

10094 19-13 

1-0235 12-38 







Oxalic acid 

Arsenic acid 










Tartaric acid 

Phosphoric acid 

Chloride of sodium 

Considerable latitude thus appears to exist in the diffusibi- 
lity of the different acids. To make the result for nitric acid 
fairly comparable with that for hydrochloric acid, the former 
should be increased in the proportion of 5'i to 63, that is esti- 
mated as nitrate of water. .This calculation gives 33*5 ars. 
of nitrate of water diffiised, which approaches closely to S^'l 
grs., the quantity for chloride of hydrogen or hydrochloric 
acid. The quantity of soda neutralized by the sulphuric and 
hydrochloric acids diffused was as 14-*32 to 28"97, or nearly 
as 1 to 2. Sulphuric and acetic acids, on the other hand, 
appear to be equally diffusible. Phosphoric acid is the least 
diffusible acid in the series, presenting only about half the 
diff'usion product of the two last-mentioned acids. The solu- 
tion of phosphoric acid had been boiled for half an hour be- 
fore diff'usion, and was therefore in the tribasic state. The 
same precaution was not thought of for arsenic acid, although 
it is possibly required by this acid also. These two acids do 
not exhibit the equality of diffusion anticipated from their 
recognized isomorphism, but it is to be stated that the acidi- 

Phil. Mag, S. 3. Vol, 37. No. 249. Sept, 1 850. O 

194 Prof. Graham on the Diffiision of Liquids. 

metrical method of analysis followed is not so properly appli- 
cable to these two acids as it is to all the others. 

3. Diffusion of Ammoniated Salts of Copper, 

It was interesting to compare together such related salts as 
sulphate of co})})er, the aumioniated sulphate of copper or 
soluble compound of sulphate of copper with 2 equivs. of am- 
monia and the sulphate of ammonia. It is well known that 
metallic oxides, or subsalts of metallic oxides, when dissolved 
in ammonia or the fixed alkalies, are easily taken down by 
animal charcoal. This does not happen with the ordinary 
neutral salts of the same acids, which are held in solution by 
a strong attraction. Supposing the existence of a scale of the 
solvent attraction of water, the preponderance of the charcoal 
attraction will mark a term in that scale. And if the solvent 
force is nothing more than the diffusive tendency, it will follow 
that salts which can be taken down by charcoal must be less 
diffusible than those which cannot. 

Of sulphate of ammonia and sulphate of copper, solutions 
were prepared, consisting of 4 anhydrous salt to 100 water, 
the sulphate of ammonia being of course taken as NH'^O, SO^. 
The solution of the copper salt was divided into two portions, 
one of which had caustic ammonia added to it in slight excess, 
so as to produce the azure blue solution of ammonio-sulphate 
of copper. 

The solutions were diffused for eight days^ at a mean tem- 
perature of 64"'9 for the sulphates and nitrates, and 67°*7 for 
the chlorides. 

Table VI. — Diffusion of solutions, 4 salt to 100 water. 

Density of solution 
Name of salt. at temperature of 
' experiment. 

Anhydrous salt 
diffused in grains. 

Sulphate of ammonia 




















Sulphate of ammonia 

Sulphate of copper 

Sulphate of copper 


Ammonio-sulphate of copper 

Ammonio-sulphate of copper 

Nitrate of ammonia 

Nitrate of ammonia 

Nitrate of copper 


Nitrate of copper 

Ammonio-uitrate of copper 

Ammonio-nitrate of copper 

Chloride of ammonium 


Chloride of ammonium 

Chloride of copper 

Chloride of copper 

Ammonio-chloride of copper 

Ammonio-chloride of copper 

Prof. Graham 07i the Diffusion 9f Liquids. 195 

It is to be observed, that in preparing the ammoniated salts, 
the solutions of the neutral salts of copper were slightly diluted 
by the water of the solution of ammonia added to them, so 
that the proportion of salt of copper which they possessed was 
sensibly reduced below !• per cent. On the other hand, the 
copper salt which diffused out is estimated, not as ammoni- 
ated, but as neutral salt. It will be observed that the quantity 
of sulphate of copper diffused out in the experiments falls from 
6'35 in the neutral salt to 1'44' gr. in the ammoniated salt; 
of nitrate of copper from 9*77 to 1*56, and of chloride of cop- 
per from 10"65 to 4'24'. These numbers are to be taken only 
as approximations ; they are sufficient however to prove a 
much reduced diff'usibility in the ammoniated salts of copper. 

It will be remarked that the nitrate of ammonia and chlo- 
ride of ammonium approximate, 15*80 and 16*59 grs. ; as do 
also the nitrate and chloride of copper, 9"77 and 10*65 grs.; 
the chlorides, which were diffused at the higher temperature 
by 2°"8, exceeding the nitrates in both cases. 

4. Diffusion of Mixed Salts. 

When two salts can be mixed without combining, it is to 
be expected that they will diffuse separately and independently 
of each other, each salt following its special rate of diffusion. 

(1.) Anhydrous sulphate of magnesia and sulphate of water 
(oil of vitriol), one part of each, were dissolved together in 10 
parts of water, and the solution allowed to diffuse for four 
days at 61°-5. 

The water-jar was found to have acquired — 

Sulphate of magnesia . . . 5*60 grs. 
Sulphate of water .... 21*92 grs. 

27*52 grs. 

The experiment with the same diffusion cell and liquid 
being continued for a second period, this time of eight days, 
there was found to be simultaneously diffused, of — 

Sulphate of magnesia . . . 9*46 grs. 
Sulphate of water .... 29*32 grs. 

38*78 grs. 

It is obvious that the inequality should be greatest in the 
first period of diffusion, or with the initial diffiision, as it ac- 
tually appears above, and become less and less sensible as the 
proportion of the low diffusive salt comes to be increased in 
the solution phial. 

In former experiments upon the solution of sulphate of 


196 Prof. Graham on the Diffiision of Liquids. 

magnesia alone in water, as 1 salt to 10 water, compared with 
sulphate of water, also as 1 to 10, the disparity in the diffusion 
ot" these two salts was less considerable, beintr only as 1 to 
2-385, instead of 1 to 3 or 4. 

(2.) A solution was also diffused of 1 part of anhydrous 
sulphate of soda and 1 part of chloride of sodium in 10 parts 
of water, for lour days at 61°'5. The salt which diffused out 
in that time consisted of — 

Sulphate of soda .... O'l'S grs. 
Chloride of sodium . . . 17*80 grs. 

27-28 grs. 

The sulphate of soda in the last experiment had begun to 
crystallize in the solution phial, from a slight fall of tempera- 
ture, before the diffusion was intcrruj)ted, a circumstance 
which may have contributed to increase the inequality of the 
proportions diffused ot these two salts. 

(3.) A solution of equal weights of anhydrous carbonate of 
soda and chloride of sodium, namely, of 4 parts of the one 
salt and 4 parts of the other, to 100 water, was diffused froui 
3 four-ounce phials of 1-25 inch aperture, at a mean temj^e- 
rature of 57^*9 and for seven days. The diffusion product 
amounted to 17-10, 17-58 and 18-13 grs. of mixed salt in the 
three experiments. The analysis of the last product of 18*13 
grs. gave— 

Carbonate of soda . . . 5-68 31*33 

Chloride of sodium . . 12-45 68*67 

18-13 10000 

Here the carbonate of soda presents a diffusion less than 
one-half of that of chloride of sodium. The difference is again 
greater than the peculiar diffusibilities of the same salts as 
they appear when the salts are separately diffused. For in 
experiments made in the same phials with solutions of 4 parts 
of each salt singly to 100 water, but with a lower temperature 
by 3'*6, namely, at 54-3, the diffusion product of the carbo- 
nate of soda was 7-17 and 7-34 grs. in two experiments, of 
which the mean is 7-25 grs. ; while the diffusion product of 
the chloride of sodium was 11*18 and 10*73 grs. in two expe- 
riments, of which the mean is 10'95 grs. The quantity of 
chloride of sodium diffused being taken at 100 in both sets of 
experiments, we have diffused — 

Of carbonate of soda 66-18, when diffused singly. 
Of carbonate of soda 45-64, when diffused with chloride of 

Prof. Graham o)i the Diffusion of Liquick. 197 

The least soluble of the two salts appears in all cases to 
have its difFusibility lessened in the mixed state. The ten- 
dency to crystallization of the least soluble salt must evidently 
be increased by the admixture. Now it is this tendency, or 
perhaps more generally the increased attraction of the particles 
of a salt for each other, when approximated by concentration, 
which most resists the diffusion of a salt, and appears to 
weaken the diffiisive force in mixtures, as it is also Ibund to 
do so in a strong solution of a single salt. 

(4.) Equal weights of nitrates of potash and ammonia dis- 
solved, as in certain preceding experiments, in five times the 
weight of the mixed salts of water, and diffused for eight days, 
gave in two experiments — 

At o9='-4. htb'-Z°Q. 

Nitrate of potash . . . 28-39 25-S8 

Nitrate of ammonia . . 36-16 30-36 

Q^'55 56-24 

The inequality in the diffiision of these two nitrates is sin- 
gular, considering that in solutions of 1 salt to 10 water, they 
appeared before to be equally diff'usive. But on now com- 
paring the diffusion of solutions of 1 salt to 5 water, at 52°-6, 
the salts no longer diff'used in equal proportions : — 

Nitrate of potash gave . 57-93 grs. 
Nitrate of ammonia gave 82*08 ars. 

The solution of nitrate of potash last diffused was nearly a 
saturated one, while that of nitrate of ammonia is far from 
being so. The first has its diffusibility, in consequence, im- 
paired, and falls considerably below the second. 

The relatively diminished diffusibility of sulphate of mag- 
nesia, when associated with sulphate of water, is probably 
connected with a similar circumstance ; sulphate of magnesia 
being less soluble in dilute Sulphuric acid than in pure water. 

(5.) The salt which diffused from a strong solution of sul- 
phates of zinc and magnesia, consisting of 1 part of each of 
these salts in the anhydrous state and 6 jiarts of water, did 
not consist of the two salts in exactly equal proportions. The 
mixture of salts, diffused for eight days, as in the late experi- 
ments, gave the following results : — 

Sulphate of zinc . . 
Sulphate of magnesia 

16-80 16-09 16-87 

There is therefore always a slight but decided preponde- 
rance of sulphate of magnesia, the more soluble salt, in the 

Exp. I. 









198 Mr. T. S. Davies on Geometry and Geometers. 

diffusion product. These last experiments were made at an 
early period with another object in view, namely, to ascertain 
whether in closely related salts, such as the present sulphates 
of magnesia and zinc, the two salts might be elastic to each 
other, like the particles of one and the same salt, so that one 
salt might possibly suppress the d illusion of the other, and 
diffuse alone for both. The experiments lend no support to 
such an idea. 

It appears from all the preceding experiments, that the in- 
equality of diffusion which existed, is not diminished but ex- 
aggerated in mixtures, a curious circumstance, which has also 
been observed of mixed gases. 

[To be continued.] 

XXIV. Geometry and Geometers. ' 

Collected by T. S. Davies, Esq., F.Ii.S. and F.S.A.* 

No. VI. 

A S 1 have had frequent occasion to speak of Dr. Matthew 

'^^ Stewart in the earlier portion of these papers, it will be 

proper here to make one statement more. 

From the character of his General Theorems, I have long 
entertained the opinion that Dr. Stewart had discovered a 
considerable number of Porisms besides those printed in his 
book, and the two he gave to Dr. Simson. The description 
of his MSS. given by Playfair, in his memoir of that illus- 
trious geometer, led me to believe that it would be possible 
to make out not only the propositions but likewise their de- 
monstrations, somewhat in the manner that I did with the 
Porismatic part of his General Theorems in the Edinburgh 
Transactions a few years ago. I consequently applied to 
an eminent mathematical archaeologist to obtain for me infor- 
mation as to what had become of those papers, and whether they 
were accessible for such a purpose. In a short time he sent me 
the copy of a letter from the proper custodian of the papers, 
decisive on this head. T/icy are all destroyed — deliberately 
burnt; and not only his, but likewise all the MSS. of his son 
Dugald Stexoart. Into the motives for this act, which its perpe - 
trator offers, I will not enter ; and shall only state that he was a 
descendant of those two men whose writings he has thus irre- 
trievably destroyed. I have thought it desirable to put upon 
record this fact : for though public indignation will not restore 
the lost treasures, it may prevent others from imitating the 

A great portion of the correspondence with Nourse and 
* Communicated by the Author. 

Mr. T. S. Davies 07i Geomet7'y and Geometers. 199 

his successor Wingrave is of tlie most ordinary business cha- 
racter. This might be expected. A few passages even in the 
dreary Hst of £ s. d. are not without interest. 

For instance, the ■price of authorship'. — Mr. John Landen 
thus writes (Aug. i!8, 1758) to Nourse, after describing liis 
" Residual Analysis^:" — 

" I would have it very elegantly printed in quarto, (with Wood or 
Tin Cut?) upon such j^aper and Avith such letter as my Lucubrations. 
If you chuse to purchase the copy you shaU have it for less than I 
would take of any^other person. 

"The subject is very interesting, and I p ... ne [illegible — pre- 
sume ?] a considerable number will be speedily sold ; therefore ex 
pect you will not give me less than two Guineas per sheet. How- 
ever I shall leave it to you to pay me according as it shall sell." 

It proved here, as it often does, that an author is himself 
the very worst judge of what will " sell." Nobody but system- 
atic collectors of classes of books, knows anything of Lan- 
den's Discourse on the Residual Analysis, except accidentally 
by mere name. The philosophy of Landen "never took;" 
and the truths delivered, or professedly deduced by means of 
it, were neither new nor in any way remarkable. Still the 
book was not without merit ; nor the author destitute of very 
high mathematical powers. He was not, however, deficient 
in the amour 2>ropre ; but, on the contrary, was remarkable 
for carrying out the principle to an extreme degree. 

Dr. Gregory (who from being " bred and born " in the 
neighbourhood of Peterborough was likely to be well ac- 
quainted with the gossip of the place) has informed me that 
Landen was a man of "imposing presence and imperious man- 
ners." He was steward to Earl Fitzwilliam, for that nobleman's 
Northamptonshire estates. The then countess, who appears 
to have much disliked the bearing of the steward, described 
an interview between him and her liege lord, as that "between 
Lord Landen and his steward Mr. Fitzwilliam." 

Landen was perhaps the only non-academic mathematician 
F.R.S., who did not join with Horsley, Hutton, and the other 
seceders from the Royal Society on the accession of Sir 
Joseph Banks to the chair. Philosophy in the Society had 
then degenerated into Faction: a sort of scientific imitation 
of Whig-and-Toryism. The contest was one of partisanship, 
and it was conducted in the true spirit of political party. 
The naturalists have censured the mathematicians, and the 
mathematicians the naturalists, for their conduct in that dis- 
creditable dispute. The question has descended even to our 

200 JNIr. T. S. Davies on Geometry and Geometers. 

own (lay ; and it has very recently been mooted in the Philo- 
sophical Ma<i;azine. It was a scene which showed nndeniahly 
the decadence olthe philosopliic spirit in the Society, rather 
than the overriding of one branch of science by another; 
although it has been almost uniformly represented that the 
"mathematical sciences were ousted iVom the Society by the 
overwhelmin<r influence of the naturalists." The terms them- 
selves were mere syvibols oj' partij: but we are not to assume 
that mathematical science was excluded from the Society be- 
cause Dr, Horsley was foiled in his aspirations for the Chair, 
and Dr. Mutton divested of the Foreign Secretaryship. Tl)e 
" little band " overrated their influence in the Society ; and 
the time is come when some definite idea of their mathematical 
powers and pretensions can be formed, quite independently 
of factious prejudices. It would be well, therefore, to judge 
the question apart from all party considerations. 

That Horsley had as good a claim to the Chair as Banks, 

f'lere is no doubt: but he attempted to carry his purpose on 
ctitious grounds — as the representative of the mathematical 
section of the Society. That his claims, however, were not 
overwhelming, but only comparative tcifh those of his compe- 
titor^ no mathematician will now venture to assert. Every 
work he published is " completely shelved," and no one, I 
believe, reached a second edition. His name indeed is only 
remembered in scientific circles by his connexion with these 
unhappy disputes. That his supporters and fellow-sece- 
ders were so many Newtons and Halleys, who will assert, 
even though the names of Maskelyne, Maseres and Hutton 
were on that list? Waring, Milner, Landen and others, kept 
aloof from all share in such a partisan-system of enforcing the 
superiority of the mathematical sciences over those of obser- 

So much has been said on the other side that it does not 
become me to speak upon it. I am no judge of the scientific 
merits of the actors in it. Of the long period of " misrule" 
which followed, I have only to say that something of the kind 
might have been expected : the reign of " naturalism " was the 
reign of actual conquest — the conquest of a faction bearing 
one symbol over another faction bearing another symbol. 
Perhaps the political condition of Ireland at this moment is 
only the same history on a larger scale. 

1 have been tempted into this long digression, from the 
consideration that it is high time that disputes of so long 
standing should be looked at apart from the symbols of the 
respective parties — symbols to which the actors on either side 
had little claim. It is certainlv absurd enough that because 

Mr. T. S. Davies on Geometry and Geometers. 201 

two sets of aspiring parties quarreled " over a bone " some 
eighty years ago, that men who cultivate two very difficult 
and ever-expanding sciences, should no'-iSo look upon each other 
with jealousy, because those two Tactions assumed the names 
ot these two sciences as the symbols of their factions. Even 
as regards the suppression or publication of papers in the 
Philosophical Transactions, it will be more frequently found 
that any impropriety has arisen from the influence of persons 
pursuing the same science than the opposite one — at any rate 
the alleged impropriety. 

Another writer proposes to Nourse to take a work on his 
own hands, under the title of Syntagma Analyscos : or a New 
Introduction to the Mathematics. After a laudatory account 
of himself, he gives the contents, and concludes with the fol- 
lowing: — 

" As I often write to the Diaries, Magazines &c. under various 
fictitious appellations, 1 may thereby forward its sale by recomniend- 
, ing or quoting it." 

The method of indirect puffing was not unknown even 
then ! Till I met with this letter, liowever, I had taken the 
name of the writer (Malachy Hitchins, Exeter College, Ox- 
ford) to be itself fictitious. His contributions (at least under 
his own name) are respectable for the time, though none of 
them bespeak powers far above mediocrity. I do not think 
that Nourse was taken with the bait of his " recommending " 
his own book ; and indeed I have no knowledge of its having 
been published at all. 

The following passage is only curious as showing a mathe- 
matician's notions of ainusement. It is from a printed pro- 
posal to publish by subscription a " Complete Course of Ma- 
thematics " in 96 sixpenny numbers ; the scheme of which 
was abandoned, and the MS. offered to Nourse, who also ap- 
pears to have declined it. 

" Even to those who peruse books for amusement, the author 
ventures to recommend this work, presuming that more real enter- 
tainment, much more genuine satisfaction must flow from it, than 
can arise from an insignificant romance or fictitious tale, which serve 
chiefly to vitiate the taste and corrupt the morals." 

This is dated Newcastle 1770, and the author is John Da- 
vidson — a mathematician of great local note, and of some ge- 
neral reputation in those days. 

202 Mr. T. S. Davies on Geomefri/ and Geometers. 

A letter from Mr. Andrew Marshall, dated Dover, Oct. 9, 

177'5, contains a proposal to Nourse to take a translation of 
the first three books of Sijusoiii Sect. Con., or a complete 
translation ot the whole work, if Nourse should prefer it. The 
letter is valuable in one respect, as giving a reason for this 

" It was at the request of Dr. Matthew Stewart and Dr. William- 
son professor of Mathematics in the Universit)' of Glasgow, that I 
undertook that translation : and the reason why they interested 
themselves in it was, that they thought their colleges were not so 
well attended, while the students were obliged to read a latin book 
on so abstruse a subject, as they would be, was the text book in 
English and at a lower price." 

The translation — at least so I judge, but at any rate a trans- 
lation — was published in Edinburgh by Charles Elliott, in 
1775. Nourse's name does not appear among the London 
publishers on the title-page. It had been well for English 
science if all the books that Simson and Stewart ever wrote 
had been printed in our own language. 

Trinity College, Dublin, has been, perhaps, the most tena- 
cious adherent to the use of Latin in its lectures, exercises and 
responsions. Amongst the works published for the use of that 
college was Dr. Hugh WvunWioxr^ Scctiones Conicce, 4to, 1758, 
in Latin. This work, however, though compulsorily read in 
college, was otherwise slow in its sale — -much slower indeed 
than its great merit would have led us to expect. In a letter 
to Nourse in 1768, he says, "there were 600 copies printed, 
and about 100 of them remained " then in Dublin; whilst he 
speaks of 230 copies in the hands of Johnston, the London 
publisher. These last, with the copper-plates and copyright, 
he offers to Nourse, and ultimately appears to have sold them 
to him, with all else relating to the work, for two shillings 
per volume, though he says the print alone cost him more 
than three shillings per copy. He adds : — 

" You were certainly right in supposing that the treatise would 
have sold much better had it been written in EngHsh, for Johnston 
told me two years after it was published that he was sure he might 
in that time have sold almost the whole impression had it not been 
in latin. This makes me imagine that when you get the Property 
of Work (and the copperplates which cost me 20£) it may be wortlx 
your while to publish a Translation sometime hence, a Person of 
tolerable skill would translate such a Book as easily as he could 
transcribe it." 

He then goes on to mention the additions he would make 

Mr. T. S. Davies on Geometry afid Geometers. 203 

to it, in the form of an appendix, when translated. This, how- 
ever, in a subsequent letter he proposes to replace by a few 
occasional scholia. Nourse appears to have sent him the 
translation in MS.; which, though so easy to make, he con- 
sidered to be very faulty, and an amended translation in its 
turn was only somewhat less faulty. It ended in two Trinity 
men, who were reading for fellowships, recommended by 
Dr. Hamilton, being employed. Their remuneration was ten 
guineas ! 

The following is one of the most singular facts, perhaps, in 
Irish Church history: — 

" Let him [his friend Matthew Raper] know I would write to him 
had I any thing worth communicating, further than one thing (which 
I know his friendship to me will make him pleased with) that I have 
very fortunately and witJiout any solicitation of mine got the Deanery 
of Armagh, the best preferment in our Church under a Bishoprick and 
equal in value to some of them." (Letter, Ap. 30, 1768.) 

The worthy Dean views his good fortune under a sufficiently 
worldly aspect : and a fair share of worldly tact is shown in 
the following extract from another of his letters (Nov. 23, 

" It is proper to observe to you that the Euclid to which my cita- 
tions refer is Whiston's latin edition of Tacquet's Euclid. And I think 
it will be proper to apprize the reader of this at the end of the Trans- 
lator's Preface, for I am of your opinion that such a preface will be 
absolutely necessary, since you cannot avoid saying in the Titlepage, 
Translated from the Latin. I think you or any one that is acquainted 
with the work might very easily write such a preface ; as nothing 
more would be necessary than to say that the following Treatise 
written in Latin was published at such a time and has since been 
so well received by the learned that the Professors in the several uni- 
versities in England and Ireland have used and recommended it in 
preference to all others on the same Subject, and therefore the 
Translator thought that an English Edition would be an acceptable 
Present to the Public in a Country where so many had distinguished 
themselves by their great proficiencj' in mathematical studies tho 
they had not much cultivated the learned languages. He might 
then (^0 shoiv he laid read other works of this kind) mention some of 
the Particulars in which he thought this work had the advantage of 
others. He might say some thing in general of the Method or plan 
upon which the Author proceeds, and his manner of executing it, 
and then for a further account of the method refer the Reader to the 
Author's Preface which follows. 

" I have only mentioned these hints to show what a Preface of 
this sort usually contains and that there can be no great difficulty in 
drawing it up. And I dare say if you were to write to Mr. Wil- 
liamson or any other Teacher who has read the Book and communi- 

204- Mr. T. S. Davies on Geomctvi/ and Geometers. 

cate these hints as ijour own thoughts, and request his assistance he 
would very soon draw up a Preface to your purj)ose, and you might 
liave it in your power to oblhjc him again." 

"Secrets in all trades hut mine /" The learned author and 
the liberal bookseller combine to represent a mere speculation 
ol their own as the act and jud<^emenl ot" the "translator," — 
that invisible, if not imaginary, personage of all ages as well 
as our own. 

It does not appear who did draw up the " translator's pre- 
face:" but it is executed pretty closely in accordance with the 
above prescription ; and some changes are introduced into the 
text as suggested by Dr. Hamilton, which form real improve- 
ments upon an already valuable treatise. 

It seems somewhat strange tlmt Dr. Abram Robertson 
should print a ponderous 4to in seven books, only a few years 
after (1792), also in Latin^ and very much on the same plan 
as those of Simson and Hamilton, though more closely imita- 
ting the latter. The necessity that was felt, even b}' authors 
and publishers, for putting the scientific works they issued in 
a language which could be read by all, had j)roduced no in- 
fluence at Oxford ; but even there it was ultimately felt to be 
absolutely necessary to give an English edition of at least a 
part of the work, which was accordingly done in 8vo a few 
years afterwards. 

Even Euclid was recently read in Latin in the Dublin Col- 
lege; but as it has since been translated, I presume it is 
now* read there in English. Dr. Elrington's edition, which is 
there used, differs a good deal from Simson's, but most of all 
in the treatment of j)roportion : but 1 only refer to it here as 
another instance of the paramount necessity for writing all 
books on science in our vernacular tongue. 

By some letters from the Rev. Francis Holliday, Rector of 
West Marsham, Notts, it appears that the price paid for the 
copyright of that gentleman's Fluxions was twenty-three 
guineas ; that is, 07ie guinea per sheet. ( Letter to Nourse, con- 

* Since this was written, a Dublin friend whom I had asked about the 
viotive for the retention of Latin as the medium of so much of the Trinity 
College exercises, " wonders where I could have met with so antiquated a 
thing as a Latin Euclid used in the College." My own copy is marked 
" editio quarta, 1813." The Latin appears to be still the medium of ex- 
amination for the junior fellowships ; though (judging from the Dublin 
University Calendar) dispensed witli in the degree examinations. This 
traditionary practice is hence gradually " wearing out " even in its last 
stronghold; and certainly in the case of fellowship examinations, less ex- 
ception can be taken to the practice, tlian in the case of degrees, whether in 
honours or not. 

Mr. T. S. Davies on Geometri) and Geometers. 205 

taining a statement of accounts, Nov. 22, 1777.) He asked 
thirty guineas, and estimated it at seventeen or eigliteen sheets ; 
see letter, Sept. 26, 1770'. Fhixions were cheap then, but 
they command no price at all now. 

It may be worth noticing, that Dealtry's is the last book 
published with the name and notation of Fluxions in this 
country; but Jephson's the last with the name only, having 
the notation of Leibnitz instead of Newton's ; the former in 
two successive editions, and the latter in two volumes issued 
at different times. The eleventh edition of Ilutton's Course 
is, however, the last English book in which either the 
name or notation appeared (1835, 1837); and though I 
strongly urged upon Dr. Gregory, who acted as principal 
editor of that edition, the necessity for a change, I failed to 
convince him. This was the more inexplicable to me, as he 
had for many years admitted the language and notation of the 
Differential Calculus (though, perhaps, not its metaphysics) 
into the Ladies' Diary, of which he was the editor. It first 
appears in 1824 in the Diary*. His argument for retaining 
it in Hutton's Course was, that Dr. Hutton himself would 
have insisted on its retention ; and he felt himself bound in 
honour to make no further changes in that work than the 
author himself would liave made under the same circum- 
stances, and with a full knowledge of the state of mathematical 
science in 1836. As I am personally interested in this ques- 
tion, I may be allowed to state that I consider that view to 
have been a mistaken one; and that a resolute adherence to 
what it was supposed Dr. Hutton would have done, has driven 
the work " out of the market." The ultimate changes made 
in it came too late; and yet no man was more eminently qua- 
lified to make them than Dr. Gregory. 

It appears from letters written in 1811 to Wingrave (suc- 
cessor to Nourse) by Miss Maskelyne, that the Greenwich ob- 
servations were the private propertij of Dr. Maskelyne. Tliey 
are claimed as such ; and Sir Joseph Banks's authority is 
quoted in support of it. Yet the Board of Admiralty paid 

* See two interesting papers on the Introduction of the Notation of the 
Differential Calculus into thij Country' by an eminent anonym^, and by Mr. 
Wilkinson, in the Mechanics' Magazine for 1849. It may, however, be 
remarked, that Dr. Gregory introduced the differential notation into his 
Trigonometry (using the S instead of the d) as far back as 1816; and that 
to the edition of Hutton's Course of (vol. ii.) 1837, he gave a translation, 
literally, of a portion of Lubbe's treatise. 1 am not able at this moment to 
give the dates of either Dealtry's or Jephson's works; but the former 
ranged somewhere from 1812 to 1814, and the latter a little before and 
after 1830. 

20G Mr. T. S. Davies on Geometry and Geometers. 

for paper, print, iiislrunieiits, and a salary for making those 
observations ! Many strange affairs, liowever, have occurred 
with respect to books printed by the Admiralty ; to some of 
which I may hereafter direct more particular attention — rela- 
ting, of course, to "by-gone days." 

It seems that even 80 or 100 years ago the booksellers pub- 
lished a good deal "on conmiission " for the authors: but 
they do not seem to have carried this kind of business to the 
extent that we see it in our day, nor to have charged quite so 
heavily for their services as we now find to be the case. Nor 
do they appear to have been so eager for that kind of business 
as their successors have become. 

A Mr. John Wright of Edinburgh, a friend of Marshall's, 
sent 100 copies of a work on Trigonometry (intended as a 
supplement to Simson's Euclid) to Nourse in 1772 for sale. 
In 1783 it appears that copies to the amount of six guineas 
had been sold : and that the " charges " against this were 
three pounds seventeen shillings ! 

Many large works that have appeared were first published 
by public subscription. Usher's Astronomy, Vince's Astro- 
nomy, Horsley's Newton*, Taylor's Tables, and some others, 
are matters relative to which there is more or less correspond- 
ence in this mass of papers. A memorandum by Wingrave 
respecting one work, the name of which I cannot decipher, is 
" not enough sold to pay the advertisements." 

Several papers of Emerson's occur amongst Mr. Maynard's 
collection, but none of them of much scientific importance ; 
and, indeed, all that is of any value was subsequently incor- 
porated with his published works. Flis books are even now 
ubiquitous, and his name is familiar to every tongue; and 
hence quotation would be idly superfluous. In fact, but for 
the purpose of correcting a very general popular error with 
respect to him, his name might have been altogether omitted 
from these papers. 

Emerson wrote nearly twenty works in all, and upon all 
subjects, into the service of which such mathematics as he 
possessed could by any contrivance be pressed — from arith- 
metic to increments, fluxions, mechanics, architecture, music 

* It appears from a printed list tliat florsley had obtained 369 subscri- 
bers : crowned heads, nobility, personages in high civil and diplomatic 
offices, university and college libraries — in short, the <7i/e of Europe. A 
less pompous and less pretending editor (though as competent to the un- 
dertaking, as Horsley was confessedly incompetent) must have sought his 
patrons elsewhere, and have been satisfied with a smaller number of them. 

Mr. T. S. Davies on Geometry and Geometers. 207 

and chronology. A few of his works (and few only) display 
a certain amount of rough invention : but he was singularly 
confused in his development of a process, and one of the most 
uncouth of all the mathemalical writers of this country. It is 
very probable that, al)ating the Metliod of Increments (which 
owed its value to its being then the only one in our language, 
Dr. Brook Tayloi"'s being in Latin and untranslated), his 
most useful works have been the Elements of Geometry and 
the Conic Sections. The former contains a few theorems 
which are, as far as I know, original*; and the latter is va- 

* It is often extremely difficult to decide respecting originality in ele- 
mentary investigations ; for no one can undertake to look carefully through 
every elementary book that has been published, to ascertain whether some 
particular and simple proposition might not possibly be contained in it. 
Nevertheless some general criteria might be laid down, which would contri- 
bute towards probability on one side or another in most cases ; and this 
presumed probability would often limit the trouble of the search to very 
narrow bounds. Almost every proposition naturally refers itself to a class j 
and if once observed, others of that class must soon follow. If, then, upon 
our observing such a proposition we find it isolated, it is highly probable 
that it originated with the author who there gave it, or at least not long 
"before. In the few cases which I have had occasion to examine minutely 
and carefully, I have rarely found this rule to fail — indeed, in no one to 
signally fail. This, too, is precisely the same in respect to analytical de- 
vices — and not widely different is the testimony of the history of experi- 
mental science. 

This remark is made in consequence of a property of the triangle, now 
universally known, which appears to have been first given in an elementary 
treatise by Emerson {Geom., b. ii. pr. 32, 1763). "The perpendiculars 
from the angular points of a triangle to the opposite sides, pass through 
the same point.'' The property was, however, enunciated by Mr, Thomas 
Moss, an exciseman and able geometer, in 1751 ; and two neat demonstra- 
tions given to it shortly after by a writer who signs 20<I>02 (probably 
Simpson), and by Edward Rollinson, in Turner's Mathematical Exercises. 
A property still more general had been given four or five years previously 
in the Mathematician, edited by Rollinson. The less general property 
was not, however, perceived, to be deducible from the more general one, 
and both passed without further remark than the mere solutions till atten- 
tion was called to the system of connected inquiries in the Mathematical 
Repository (vol. vi.), under one aspect; and under another in the Phil. 
Mag., vol. ii. p. 26,2nd Ser., and the appendix to the Ladies' Diary, 1835. 

It may seem strange that so simple a property, and so many others similar 
or related to it, should have been unobserved by the antients, and by their 
earlier followers after the revival of letters. It must be recollected, how- 
ever, that the Greek geometers only valued a theorem (or even a Porism) 
except so far as it contributed to the solution of a problem. There are 
no traces, nor even intimations, of their having regularly attempted to form 
classed collections of theorems, or to arrange systematically the many 
beautiful series of properties of figures that could not fail to have presented 
themselves during the solution of problems. Such properties were only 
selected as would be actually required in demonstrating the constructions 
of the cases of a problem. Of these the seventh book of Pappus is a col- 
lection of instances. The properties of the ap^rjXov given by him, form 

208 Mr. T. S. Dnvies on Geometrj/ and Geometers. 

luable for tlie great number of" properties which the author 
has brought together, of which a fair portion were original. 
As ^^conicfn/, however, both works are extremely impure, every 
geometrical dilliculty being unceremoniously got over by an 
algebraical ecjuation — a }n'actice only too common amongst 
the so-called geometrical writers of our own time. This, 
however, is not the geometry becjueathed us by the Greeks, 
and exem|)lified by the Andersons, the Gregories, the Halleys, 
the Simsons, and the Stewarts of these isles. 

The popular error to which I referred is, that Emerson 
was the Coryplueus of the non-academic class of geometers. 
He has never been recognized by themselves as the head, the 
founder, or the leader of their class: but I suppose the fre- 
quency of his books on the stalls has led men little acquainted 
with the history of English geometry to infer that they either 
are, or have been, in great demand, and consulted as oracles. 
This never-ending reappearance is more due to the almost 
indestructible })a})er on which they were printed, and the firm 
bindings in which they were issued, than to any other cause; 
as very few of them ever reached a second edition, and a 
great number lay on the bookseller's hands at the time of 
Emerson's death. They were pushed into notice by the per- 

almost the only marked exception — or perhaps also Euclid's Porisms. We 
find at all events, extremely little (if anything, properly speaking) concern- 
ing lines meeting in a point, or points ranging in a straight line. The 
modern French geometers were the first to enter upon this class of re- 
searches with any degree of system ; and the results have justified their 
expectations, however sanguine. We need not then, after all, feel much 
surprise at finding the proj)osition in question claiming so recent a place in 
geometry ; and the same may be said of a great number of now-familiar 

Postscript, August 24. — Whilst reading the proof sheets, the Mechanics' 
Magazine of this date reached me, containing one of Mr. Wilkinson's able 
and elaborate analyses of our English mathematical periodicals, viz. of the 
Miscellanea Curiosa Mathematica, 1745-53, edited by Holliday, whose 
name has been already mentioned. As there is one passage which renders 
a slight modification of the preceding paragraph necessary, I quote it as it 
stands — from its offering less trouble, both to myself and the printer at the 
last moment, than recomposition and resetting would do. 

Speaking of art. x.Kxix., " A new Proposition in Geometry demonstrated, 
by Mr. William Chappie," he says : — 

" This proposition is the now well-known property, that * the three per- 
pendiculars of any triangle intersect in the same point,' and although taken 
for granted in the solutions of Quest. 45 Gentleman s Diary for 1743-44; 
Quest. 260 Ladies' Uiaru, 1745-46, the honour of a formal enunciation 
and demonstration appears to be due to Mr. Chappie. The property is 
stated both for the acute and obtuse-angled triangle, ' the same demonstra- 
tion serving for both, which however is not conducted in so purely geo- 
metrical a manner as one could wish.' " He then mentions some more le- 
cent researches, which, however, need not be introduced here. 

Mr. T. S. Davies on Geometry and Geometers. 209 

tinacity of Nourse (who formed a higher opinion of him than 
was at alljust), rather than by any intrinsic merits of their own. 

Of Emerson's personal character this is not the place to say 
much ; and indeed it would be unnecessary to do more than 
refer to Hutton's Dictionary {in loco) for a description of his 
eccentricities, were it not for a von-sequitur that has been 
drawn from his and some similar cases. It surely does 
not follow that because Emerson and some others habitually 
indulged in a rough discourtesy of bearing towards otliers, 
that it arose from the nature of their studies, or inevitably 
followed from the tone of feeling generated by mathematics. 
Why not, then, charge medical studies with the same tendency 
on the ground of an Abernethy, or the legal on the ground of 
a Thurlow, belonging to those professions? The inference 
is indeed absurd enough ; but many a time in my life have 
I heard it made. 

However, I have to beg, once for all, that if the non-aca- 
demic body of mathematicians are decreed to have a head of 
their school, they may at least be allowed their own choice. 
That election would fall, without a dissentient voice, on 
Thomas Simpson. Amongst themselves, he, and not Emerson, 
virtually fills the post; and they cannot but feel aggrieved by 
hearing a man whose character they do not respect and whose 
works they seldom open, thus held up as the prototype of 

This series of notices of the Nourse papers must necessarily 
be incomplete without some account of the man who was the 
real focus of the mathematical literature of his time — now 
verging upon a century ago. I regret that few materials of a 
positive kind have fallen in my way from which I can satisfy 
so reasonable a desire on the part of my readers. Most of 
the letters are written in more or less of that dry, business- 
style, that only brings in an interesting incident now and then, 
and always casually. One series of letters, however, of a more 
familiar and intimate character, from John Robertson of 
Portsmouth (author of the Treatise on Navigation, and other 
works, and subsequently " Clerk " of the Royal Society), 
throw some light on Nourse's personal character. A few 
scraps, too, of Nourse's own geometrical speculations betoken 
a mind of no ordinary powers, and a taste in science such as 
even few professional mathematicians have evinced. 

From the frequent jocular allusions of Robertson, it would 
appear that Nourse was a grave self-possessed person, who 
nevertheless enjoyed a pun or a good joke as well as his friend 
did. A quiet pipe with its adjuncts in the shop-pai-lour seems 
to have been his sum total of indulgence. He rarely quitted his 

FhiL Mag, S. 3. Vol. 37. No. 24?9. Sevt, 1850. P 

210 Mr. T. S. Davies on Geometry aiid Geometei'S. 

business ; and when he did, it was only to go to Oxford where 
he liad relatives — a brother, Sir Charles Nourse, and a sister, 
the wife of Dr. Hornsby, the Radcliffe astronomer. One of 
tlie letters seems to imply that he was a siiort and somewhat 
corpulent man. who always fancied himself to be " wasting 
away." He was always alive to his business, and the number 
of works of which he was the publisher was unprecedented in 
his day; his undertakings appear to have been generally 
successful, and his dealings scrupulously honourable. He 
does not appear from any allusions in these letters to have 
been married : and he amassed considerable property, which 
was bequeathed to his brother and sister. 

The mathematical character of Nourse is best shown by a 
specimen of his geometry. I therefore annex two: one a de- 
monstration of the converse of Euc. v. 25, which he required 
as lemma for some emendations of a proposition on the conic 
sections in the works of Mylne and Simson ; and the other a 
remarkably simple and elegant problem in A/igelis de inf. Pa~ 
reholis. These are given precisely as I find them in the MS., 
taking in the textual corrections made by himself. 
"Lemma (Euclid v. 25 convers). 
" Si quatuor magnitudines fuerint jiroportionales, et prima cum 

quarta major fuerit secunda cum 
tertia ; erunt prima et quarta maxima 
et minima quatuor proportionalium. 
" Sint enim proportionales AF. 
BH. C & D. Et quoniam prima cum 
quarta major est secunda cum tertia. 
non erit igitur prima AF tertia C. 
sequalis, sed vel major vel minor ea. 
Sitprimomajor.fiatque ipsiC.eequalis 
AE. et ipsi D eequalis BG. et quo- 
niam tota AF. est ad totam BH. ut 
ablata AE. ad ablatam BG ergo re- 
liqua EF est ad reliquam GH. ut 
tota ad totam. Jam ipsi D. aequalis 
fiat AM. et ipsi C. sequalis BN. et 
erit MF. sequalis primse cum quarta. 
et NH sequalis secundse cum tertia. 
Estitaque MF (ex hypothesi) major 
quam NH. Sed ME sequalis est 
NG. etenim ipsarum utraque equalis 
est C & D simul. Ergo, si ab in- 
sequalibus MF & NH. quarum MF 
major est, auferentur sequales ME 
M &NG.residuse erunt etiam inequales, 

nempe EF major erit quam GH. 
Sed supra ostensum est EF. esse ut 
GH ut AF . ad BH . Ergo AF major 

Mr. T. S. Davies on Geometry and Geometers. 211 

est quam BH et C major quam D. Sed ex hypothesi AF quam C 
major, ergo BH quam D & AF quam D major. Ergo AF & D 
sunt maxima et minima quatuor proportionalium. Similiter ostcn- 
demas, si ponatur prima minor quam tertia. Nam invertendo or- 
dinem proportionalium ut quarta vocetur prima & tertia vocetur 2'''"'. 
et sic deinceps. eadem erit demonstratio. (nuUo verbo mutato). 

" Prop 29. ad 36. Angelis De infinit. Parebolis p. 25 &c. ad 108. 


" Datis parallelis AB . CG, quas secit BC ad rectos angulos. data 
etiam puncto A : Ducere AG ita ut aggregatum triangulorum AFB. 
CFG equali sit spatio dato N. 

" Fiat AB in BM equali duplo spatio N. Quoniam igiturduplum 
N (vel AB in BM) equatur rectangulis ABxBF et FCxCG simul ; 
erit AB in FM equali rectangulo FC x CG. unde erit AB ad CG, 
hoc est, BF ad FG, ut FC ad FM. Patet igitur solutio, ut sequitur. 

"Fiat enim BH equalis BC. et ducta circa diametrumBM. circulo 
MKB, qui secet CH in K. et ducta KF parallela ipsi BA, quae secet 
BC in F. Ducatur AG per F. dico factum. Patel ex analysi. 


" Insuper in hac analysi patet, aggregatum triangulorum AFB . 
CFG tum fore minimum, quando linea BM minima est omnium quae 
conditionibus in analysi positis satisfaciant. Hoc autem evenit in 
illo casu ubi BM adeo parva vit, ut circulus hac diametro descriptus 
minimo secet lineam CH, sed tantum in uno puncto tangat. Fiat 
igitur HK (vel fiat BF=iCH) equalis HB et ducatur KF parallela 
AB. et ducta AF. triangula AFB . CFG simul sumpta minima facient 
spatiura quod abscindi possit a quavis linea per punctum A ducta. 

" Quod ci spatium ad construendum propositum minus sit rect- 


212 On an Instantajicous Demonstration o/'Pascal's Theorem, 

angulo ex A13 in liiieam datura CK (vel |BM) problema construi 

Though tlie determinations are very neatly given here, the 
circumstance of the double solution lias escaped his notice, 
viz. the jioint of intersection of CH with the remaining semi- 
circle, as represented by the accented letters, which I have put 
in for the purpose of showing it. It will be worth the while 
of the younger geometrical reader to examine this case, and 
discover whether this second solution be that of the proposed 
problem or of a collateral one. It involves no material diffi- 

Shooter's Hill, Aug. 15, 1850. 

XXV. An Instantaneous Demonstration of Pascal's Theo- 
rem by the method of Indeterminate Coordinates. Bij J. J. 
Sylvester, M.A., F.R.S.* 

THE new analytical geometry consists essentially of two 
parts — the one determinate, the other indetermmate. 

The determinate analysis comprehends that class of ques- 
tions in which it is necessary to assume indepejident linear 
coordinates, or else to take cognizance of the equations by 
which they are connected if they are not independent. The 
indeterminate analysis assumes at will any number of coordi- 
nates, and leaves the relations which connect them more or 
less indefinite, and reasons chiefly through the medium of the 
general properties of algebraic forms, and their correspond- 
encies with the objects of geometrical speculation. Pascal's 
theorem of the mystic hexagon, and the annexed demon- 
stration of its fundamental property, belong to this branch of 
the subject, and afford an instructive and striking example of 
the application of the pure method of indeterminate coor- 

Let x^ y, z, t, u, v be the sides of a hexagon inscribed in the 
conic U. Let the hexagon be divided by a new line <p in any 
manner into two quadrilaterals, say xyzf^ tuvp. 

■'■ ^^^" ayip + bxz = U = aw^ + ^tv ; 

.*. {ay — a.u)<p=.^tv—bxz\ 
.'. ay—oLU and <p are the diagonals of the quadrilateral txvz. 

By construction, sp is the diagonal joining x^ v {i. e. the in- 
tersection of A' and v) with z^ t ; and thus we see that ay — au 
is the line joining /, x with z;, z; but this line passes through 
2/, u. Therefore x, t ; y, u ', z, v lie in one and the same right 
line. Q. E. D. 

26 Lincoln's-Inn-Fields, 
August 1850. 

* Communicated by the Author. 

[ 213 ] 

XXVI. Oti a new Class of Theorems in elimination between 
Quadratic Functio7is. By J. J. Sylvester, M.A.^ FM.S.* 

IN a forthcoming memoir on determinants and quadratic 
functions, I have demonstrated the following remarkable 
theorem as a particular case of one much more general, also 
there given and demonstrated. 

Let U and V be respectively quadratic functions of the 
same 2n letters, and let it be supposed possible to institute ?i 
such linear equations between these letters as shall make U 
and V both simultaneously become identically zero f. Then 
the determinant of aU + ju.V, which is of course a function of 
A and jw. of the 2/zth degree, will become the square of a func- 
tion of A and fji, of the nth degree ; and conversely, if this de- 
terminant be a perfect square, U and V may be made to va- 
nish simultaneously by the institution of w linear equations 
betw^een the 2?i letters J. 

Let now P and Q be respectively quadratic functions of 
three letters only, say .r, j/, z; and let 

V='P+{lx + mi/ + n2)t 
V = Q + K{lx + my + nz) t. 
The determinant of aU + ju,V in respect to a?, j/, z^ t is easily 
seen to be (A + ztju,)'- x the determinant of 

K? + fj.Q-\-{lx + my + nz)t 
in respect to x, j/, z, t. Hence if we call 

aP + jxQ + (/a- + my + nz)t = W, 
and make | | . W a squared function of A, /x, or which is the 


same thing, if 

□ •iz:i{W}=o, 

X/« ' xyzt 

U and V will vanish simultaneously when two linear relations 
are instituted between the quantities (all or some of them) 
•^j Vi z, t. 

In order that this may be the case, it will be seen to be 
sufficient that 

P = Q = {lx-\-my + nz) = 

* Communicated by the Author. 

-f In the more general theorem above alluded to, the number of letters 
is any number m, the number of linear equations being any number not 

exceeding ^. 

I When n=l, we obtain a theorem of elimination between two qua- 
dratics, which has been already given by Professor Boole. 

214 Mr. J. J. Sylvester on a new Class of Theorems 

shall coexist; for then two e(|uations between <r, y, -?, of which 
l.v + 7ni/ + 7iz = will be one, will suffice to make U and V each 
identically zero. Hence we have the following theorem : 

is a factor of the resultant of 

P = Q = Lv + nuj + nz = 0. 

A comparison of the orders of the resultant and the deter- 
minant shows that they must be identical, a-ci-pics, of a nu- 
merical factor, which, if the resultant be taken in its ge>ie7-al 
lowest terms, may no doubt be easily shown to be unity. 

As an illustration of our theorem, let 


Q = cxt/ -f- a]/z + bzx. 

_| [X?-\-iJ.Q, + {lx + 7ny + nz)t} 


f A + C/^ X + biJ, I '] 

J A + fft, X + Gju, 7)1 \ 

~ I A + V X + aix. 71 I 

L / 7)1 71 J 

— 2lm{\ 4- bix){K + aiJ.) — 2})m{X + ci/,){\ + i/x) 
— 2??/(A + 0|U,)(A + rju.) 
= \^{7i- + 7)i^-]-l--2lr)i — 2))m—27il} 
+ 2\/j, { C7i- + b7n- + id- — lr)i [a + b) — 7n7i (b + c) — 7il{c + a)} 
-f /^^ { c-w- + b-7)i'^ + aH- — labhn — 2bc7)m — 2ca7il] . 
And we thus obtain, finally. 

{AP + /xQ+(/^ + w»/ + «^)/f} 

A/t xyzt 

= {ii^ + m^ + t^—2lm—2inn — 2nl) 
X {chi^ + b'^m^ + aH'^—2abl7)i — 2bc7)i7i — 2ca7il) 
— {{c/i^ -^ b))i- + al^ —lm{a + b) —7)i)i{b + c) — 7il{c + a)]^ 
= —U7)i7i[[a — b){a — c)l+ {b — a){b — c)7n -{■ {c—a)[c—b)} . 

Now to obtain the resultant of 

xy-\-yz-\-zx = 
cxy + azx + bxtj = 

Ix + 7)UJ + 71Z = 0, 

in eliviination hel'ixieen Quadratic Functions. 215 

we need only find the four systems in their loudest terms of 
A':y:z, which satisfy the first two equations, and muhiply 
the four hnear functions obtained by substituting these values 
of .r, j/, ^ in the fourth : the product will contain the resultant 
of the system affected with some numerical factor. In the 
present case, the four systems of <r, 3/, ;:; are 

.v=0 i/ = z=} 

y — - = o .v=l 

~ z — A=0 y=\ 

x—[a — h)[a — c) y={b — a){b — c) z — {c — a){c — h), 
and accordingly tlie product of 

/cTj + 7;zj/i + n::-y 

U\ + my^ + nz^ 

hnn[a — b a—cl-\-b — a.b — cm + c—ac — h.n], 

agreeing with the result obtained by my theorem, — a special 
numerical factor 4, arising from the peculiar form of the equa- 
tions, having disappeared from the resultant. 

A geometrical demonstration may be given of the theorem 
which is instructive in itself, and will suggest a remarkable 
extension of it to functions containing more than three letters, 

{k\J-^IuV -{-[lx-^my-\-nz)t]=0, 


which is a quadratic equation in A : /x, may easily be shown to 
imply that the conic aU + |U,V is touched by the straight line 

And we thus see that in general two conies, 

passing through the intersections of two given conies, 

U = V = 0, 

may be drawn to meet a given line. If, however, the given 
line passes through any of the four points of intersection, '\\t 
such case onl}' one conic can be drawn to touch it ; accordingly 

I I I I {Klj^iiM -\-{lx^my-\-nz)t) 

must be zero when Z, ?«, n are so taken as to satisfy this con- 
dition, i. e. if 

216 ISIr. J. J. Sylvester on a new Class of Theorems 




whence the theorem. 

Now suppose U and V to be each functions of four letters, 
Xf 1/, z, t; when 

I I {x\J + [j.Y+{Lv + mj/ + nz+pi)2i}=0, 


the conoid aU + jw-V touches the plane 

Ix + my + nz -\-2)t = ; 

and I I =0 being a cubic equation, in general three such 
conoids can be drawn. 

Considerations of analogy make it obvious to the intuition, 
that in the particular case of two of these becoming coinci- 
dent, the given plane Ix + my + nz +pt must be a tangent plane 
to those two coincident conoids at one of the points where it 
meets the intersections of U = V = 0; /. e. 

Ix + my + nz+pt=0 

will pass through a tangent line to, or in other words, may be 
termed a tangent plane to the intersections. Hence the fol- 
lowing analytical theorem, derived from supposing g^ r, 5, t 
to be proportional to the areas of the triangular faces of the 
pyramid cut out of space by the four coordinate planes to 
which X, y, z, t refer. As these planes are left indefinite, 
q, r, 5, t are perfectly arbitrary. 


I. — The resL 

iltant of 



\ where U and V are functions of 
OJ X, y, z,t. 




lx-\-my->r nz +pt=0 


flfU d\J dU-] 


dy dz dt 




dV dY dV 
dy dz dt 
m n p 
r s t 

> = 0; 

which system, it will be observed, consists of three quadratic 

iti elminatio7i between Qiiadratic Functions. 217 

functions, and one linear function of .r, y, ^, /, contains the 

im IZII { ^U + n;t V + (/a- + 1117/ + ns: + pt) u } . 

Xfj. xyzt 

This last quantity is of the 4 x 3th, /. e. the 12th order in 
respect of the coefficients in U and V combined ; of the 4 x 2ih, 
i. e. the 8th order in respect of /, m, n, p ; and of the zero 
order in respect of <7, r, s, t. 

The resultant which contains it is of the (4 + 4 + 2. 4)th, 
i. e. 16th order in respect to the coefficients in U and V; of 
the (4 + 8)th, /, e. the 12th, in respect of /, m, ??, p ; and of the 
4th in respect of §', r, 5, t. Hence the special (and, as far as 
the geometry of the question is concerned, the unnecessary, I 
may not say extraneous or irrelevant) factor which enters into 
the resultant is of tlie 4th order in respect to the combined 
coefficients of U and V* ; and of the same order in respect to 
/, m, 71, p, and in respect to q, ?•, s, t. 

I have not yet succeeded in divining its general value. 

In the very particular example, of tne system, 

«a;^ + /3y- = 

lx-\-7ny-\-nz-\-'pt — Q 
ax /3j/ 0- 

cz (It 

1 m n p 

I find that the double determinant is 

(fd^a'^lB^cp'^ -'r d?iY{m^ct + I'Wf 

and the resultant is 

^c^d^u^^'^icp^ + dn^)\ {rri^a, + P^f, 

giving as the special factor 


I believe that the theorem which I have here given for de- 
termining the condition that Ix + my + 7iz + pt shall be a tan- 
gent plane tc the intersection of two conoids U and V, vizi 
that the determinant of 

x\J + 'y+{lx-\-my + nz +pt)u 

shall have two equal roots, is altogether novel. 

* And consequently of the second in respect to the separate coefficients 
of each. 

= 0, 

218 Mr. J. J. Sylvester 07i a new Class of Theorems. 

What is the meaning of all three roots of this determinant 
becoming equal, /. c. of only one conoid being capable of being 
drawn through the intersection of U and V to touch the plane 

Ix + my + 7iz-\-pt? 

Evidently (^^r vi analogize) that this plane shall pass through 
three consecutive points of the curve of intersection, i. c. that 
it shall be the osculating plane to the curve. 

If we return to the intersection of two co-planur conies, and 
if we suppose a line to be drawn through two of the points of 
intersection, the conies capable of being drawn through the 
four points of intersection to touch the line, besides becoming 
coincident, evidently degenerate each into a pair of right lines. 
It would seem, therefore, by analogy, that if a plane be drawn 
including any two tangent lines to the curve of intersection of 
two surfaces of the second degree, this should be touched by two 
coincident cones drawn throuiih the curve of intersection, and 
consecjuently every such double tangent plane to the intersec- 
tion of two conoids (and it is evident that one or more of these 
can be taken at every point of the curve) must pass through 
one of the vertices of the four cones in which the intersection 
may always be considered to lie ; and it would appear from 
this, that in general four double tangent planes admit of being 
drawn to the curve, which is the intersection of two conoids, 
at each point thereof. At particular points a tangent plane 
may be drawn passing through more than one of the vertices, 
and then of course the number of double tangent planes that 
can be drawn will be lessened. These results, indicated by 
analogy, become immediately apparent on considering the 
curve in question as traced upon any one of the four containing 
cones. For the plane drawn through a tangent at any point, 
and the vertex of the cone being a tangent plane to the cone, 
must evidently touch the curve again where it meets it. We 
thus have an additional confirmation of the analogy between 
a point of intersection of two curves and the tangent at any 
point of the intersection of two surfaces. 

I might extend the analytical theorems which have been esta- 
blished for functions of three and four to functions of a greater 
number of variables; but enough has been done to point out 
the path to a new and interesting class of theorems at once in 
elimination and in geometry, which is all that I have at present 
leisure or the disposition to undertake. 

26 Lincoln's-Inn-Fields, 
August 13, 1850. 

[ '-^19 ] 

XXVII. Proceedings of Learned Societies. 

[Continued from p. 68.] 

March 7, " f\^ ^^^ application of Carbon deposited in Gas Rc- 

1850. ^^ torts as the negative plate in the Nitric Acid 

Voltaic Battery." By Christopher Leefe Dresser, Esq. Commu- 
nicated by Thomas Bell, Esq., Sec. U.S. &c. 

In the retorts used for the destructive distillation of coal to obtain 
the carburetted ^lydrogen gas for the purposes of illumination, after 
a certain time a deposition of carbonaceous matter takes place, and 
which at length accumulates to such an extent as to fill up a portion 
of the retort with solid substance, and to line the whole with a 
coating varying from the thickness of paper to several inches. 

After describing several forms in which this substance occurs, 
and which vary considerably both in density and hardness, the au- 
thor states that he found one of great hardness, very little, if at all, 
porous, and of a stony fracture, to be best adapted for the negative 
conductor of his nitric acid battery. The most convenient form for 
the negative conductor is the prismatic, \\ inch square on the side 
and about 7 inches long, which is immersed 4- inches in the acid, 
and used with round porous cells, the zinc cylinder being 3 inches 
in diameter and 4^ inches high. 

The carbon is cut into thin plates or prisms by the machine of 
the marble cutter, at a cost of about \\d. each. The prisms may 
be easily obtained 12, l^, or 18 inches long. 

The only precautions necessary in using this form of carbon, are, 
after using the plates to immerse them for a few moments in boiling 
water, to take off the adhering acid, and then to dry them before a 
fire or in a stove. 

Having used the same plates and prisms for months, the author 
detected no deterioration of their conducting power, nor any de- 
composition or alteration. The connexion was made by soldering 
a strip of sheet copper to the zinc, and pressing this strongly against 
the carbon with a clamp. * 

Comparing these plates with plates of platinum, the author could 
detect little difference in action, but the carbon appeared rather 
superior. He states that his battery of 100 plates cost under £4, 
whilst one of platinum of equal power would have cost £60 or £70. 
From the cheapness and durability of this substance, he considers 
that it will make a valuable addition to our voltaic apparatus. 

A paper was also in part read, entitled " Experimental Researches 
in Electricity. ' Twenty-third Series. § 29. On the Polar or other 
condition of Diamagnetic Bodies. By Michael Faraday, Esq., 
F.R.S. &c. 

March 14. — The reading of Dr. Faraday's paper, entitled " Expe- 
rimental Researches in Electricity. Twenty-third Series. § 29. On 
the Polar or other condition of Diamagnetic Bodies:" was resumed 
and concluded. (See p. 88 of present volume). 

220 Royal Society. 

March 21. — Tho following letter from Mr. Addington to the Se- 
cretary was read. 

Foreign Office, March 20th, 1850. 

Sir, — I am directed by Viscount Palmerston to send to you, for 
the inlbrmation of the President and Council of the l?oyal Society, 
an extract of a letter whicli his Lordship has received from Mr. James 
Richardson, stating that in the moiitli of November last, a fall of 
aerolites had taken place on the coast of Barbary attended with a 
brilliant stream of light, which extended from Tunis to Tripoli, some 
of the stones falling in the latter city. 
I am, Sir, 

Your most obedient, humble Servant, 

H. W. Addington. 
T7ie Secretary to the Royal Society. 

'^Extract of a letter from Mr. Richardson, dated off Jerhah, 
'25th January 1850. 

"I will trouble your Lordship by the mention of the astronomic 
phenomenon which terriHed or arrested the attention of the inhabit- 
ants of the whole of this coast some two months ago. This was 
the fall of a shower of aerolites, with a brilliant stream of light 
accompanying them, and which extended from Tunis to Tripoli, 
some of the stones falling in the latter city. 

"The alarm was very great in Tunis, and several Jews and Moors 
instinctively fled to the British Consulate, as the common refuge 
from every kind of evil and danger. 

" The fall of these aerolites was followed by the severest or coldest 
winter which the inhabitants of Tunis and Tripoli have experienced 
for many years." 

The reading of a paper, entitled " Discussion of Meteorological 
Observations taken in India at various heights." By Lieut.-Colonel 
Sykes, F.U.S. &c., was commenced, but was not concluded. 

April 11. — Lieut.-Colonel Sjkes's paper, entitled "Discussion of 
Meteorological Observations in India," was resumed and concluded. 

The author adverts to a former paper " On the Meteorology of 
theDeccan," published in the Philosophical Transactions for 1835, 
and after referring to the conclusions at which he arrived in that 
communication, states that, in the discussion of the meteorological 
observations which form the subject of the present paper, and which 
were made over a very extended area, at different heights, some 
being hourly and running through several years at the same station, 
it is very satisfactory to find that they fully establish the accuracy 
of the former deductions. He remarks that, as some of the obser- 
vations now discussed were hourly records continued through con- 
siderable periods of time, an opportunity has been afforded of in- 
vestigating abnormal conditions, which the former limited number 
of diurnal observations did not permit ; and gives the following 
review of what appears to be normal and abnormal conditions. 

The annual and daily range of the barometer diminishes from the 
sea-level up to the greatest height observed, 8640 feet at Dodabetta, 

Royal Society. 221 

from a mean annual and mean daily range at Madras of 0'735 and 
0-122 respectively to O'llO and ()-060 at Dodabelta; — tiie annual 
range would appear to increase, about and beyond the nortliern 
tro]iic, as the annual range at Calcutta (not by hourly observations) 
is 0*911 ; but the diurnal range is somewhat less (0'115) than at 
^Madras. At no one of tiie places of observation, even taking the 
maximum pressure of one year with tiie niinimum pressure of another 
year, does there appear to have been a range of pressure equivalent 
to an inch of mercury ; nevertheless in the Cyclones, or rotatory 
storms, there occurs at times a range of pressure of nearly two inches 
of mercury witliin forty-eight hours ; but it is shown from a compa- 
rison of the simultaneous records on board ship, where these great 
depressions were noted, with the records at the observatories on shore, 
that the great depressions occurred within very limited areas. 

The author had formerly shown that the times or turning-points 
of ebb and flow (if the term be permitted) of the aerial ocean, 
were occasionally retarded or accelerated, although the means fixed 
the turning-points within certain limit hours; but he was not then 
aware that in the ebb or flow of the four daily tides, they ever 
retrograded or halted in their onward or retiring course. The hourly 
observations now show that abnormal conditions are of no infre- 
quent occurrence, — that the tides at times flow or ebb for four, 
five, six or even seven and eight hours (one instance at Aden of 
nine hours), — that frequent instances occur of retrograde move- 
ments for short periods of time, as if the tide had met with a check 
and been turned back; and at the turning-points there are numerous 
instances of the atmosphere being stationary for a couple of hours. 

The maximum pressure of the atmosphere is in the coldest months, 
December or January, but the mininuim pressure is not in the 
hottest months, but in June or July. The barometric readings, 
when protracted, show a gradual curve from December or January 
descending to June or July, and then ascending again to December 
or January, there being an occasional interruption in October or 
November. As the curves at Madras, Bombay and Calcutta, 
correspond, and as Madras has no south-west monsoon, while 
Bombay has a south-west monsoon, and is destitute of the north-east 
monsoon of Madras, it would appear that the general movements of 
the atmosphere are little influenced by any conditions of its lower 
strata ; but the curve of pressure would seem to have some relation 
to the sun's place in the ecliptic. 

The normal conditions of daily temperature are, that it is coldest 
in India at sunrise, and hottest between the hours of 1 and 3 p.m.; 
but the tables show many aberrations from this rule. The re- 
gular increment or decrement of mean monthly heat from the maxi- 
mum or minimum period is somewhat remarkable, as the curve is 
independent of the south-west monsoon at Bombay and the north- 
east monsoon at Madras ; and the passage of the sun twice over 
both places does not derange the curve. The anomalies of the 
annual mean temperature of Madras, Bombay, Calcutta and Aden, 
not diminishing with the increase in the latitude of the respective 

222 Royal Society. 

places, are pointed out, ami numerous instances are given of the 
very great power of the shmting rays of the sun beyond the tropic. 
As is tiie case witii the barometric, so do the heat tabh's indicate 
that the annual and daily ranges of the thermometer diminish with 
the elevation of the place of observation above the sea-level, the 
elevated table-land of tlie Deccan hosvever being an exception to 
this rule. At Mahabuleshwur, at taOO feet, the temperature of the 
air was never below 15° with a maximum and minimum thermo- 
meter; and at Dodabetta the temperature of the air was never below 
f58°*.5, nevertheless at both places ice and hoar-frost were frequently 
fountl on the ground at sunrise, resulting from the separate or con- 
joinetl effects of radiation and evaporation. 

After stating the want of confidence he has in observations of the 
wet-bulb thermometer as a means of determining the dew-point, 
and that he greatly prefers DanieU's hygrometer for this purpose, 
the author observes that he will not venture to say more with re- 
spect to normal conditions of moisture in India than that the air of 
the sea coast has always a much greater fraction of saturation than 
the lands of the interior; and that the elevated plateau of the Dec- 
can is periodically subject to very high degrees of dryness. 

Some very unexpected phenomena with reference to the distri- 
bution of rain are pointed out. It is found both on the sea coasts 
and on the table-lands of the Deccan, that within very limited areas, 
the differences in the fall of rain may be very great. With nine 
rain-gauges employed in the small island of Bombay in the months 
of June and July, in the monsoon of 1849, the quantity collected 
in the different gauges ranged in July from ^S inches to 102 inches, 
and in June from 19 inches to 46 inches. At Sattarah, in the 
Deccan, with three rain-gauges within the distance of a mile, they 
differed in their contents several inches from each other ; and at 
Mahabuleshwur and Paunchgunny, nearly on the same level, the 
latter place being only eleven miles to the eastward of the former, 
the annual fall of rain was 254- inches and 50 inches respectively ! 
The normal conditions are, that there is a much greater fall of rain 
on the sea coasts than on the table- lands of the Deccan, but that the 
Ghats intervening between the coasts and the table-lands have three 
times the amount of the fall on the coasts, and from ten to fifteen 
times the amount of the fall on the table-lands of the interior ; the 
paucity of the fall of rain at Cape Comorin and in the mouths of the 
Indus Avould also appear to be normal conditions. 

The tables must be referred to for the winds ; the normal states are 
those of the south-west and north-east monsoons, and the influence of 
the latter is periodically felt at the height of 864-0 feet at Dodabetta, 
which height would appear just at the upper surface of the stratum of 
air constituting the south-west monsoon ; but hourly observations for 
lengthened periods are necessary at Dodabetta, to determine what 
really are the periodical winds at that height. From the points other 
than those between south and west, and north and east, there is also 
at the several stations a certain amount of periodicity in the winds, 
the winds that are common to different stations having only a slant 

Royal Society. 223 

more or less at the different stations ; for instance, the south-west and 
north-west winds of Bombaj- blowing in the summer months in Cal- 
cutta incline rather to be south and north winds, than south-west and 
north-west winds ; but the author observes that to be enabled to speak 
with any precision upon this branch of the meteorology of India, and 
indeed upon most other branches with a comprehensive and philoso- 
phical object, hourly observations are necessary, — simultaneously 
taken with previously compared instruments by zealous observers ; 
and having the records in a form common to all the observers, so 
as to admit of rigid comparisons: — when this is done, not only in 
India but in Europe, meteorologists will be in a better condition 
to generalize and propound normal conditions, than the state of our 
knowledge at present would justify. 

The author states that he is indebted to that very able and zeal- 
ous meteorologist, Dr. Buist of Bombay, for the jirotracted curves 
of pressure of the l^arometer appended to his paper. 

A paper was also read, entitled " On the Structui-e and Use of the 
Liganientum rotundum Uteri, with some observations upon the 
change which takes place in the structure of the Uterus during 
Utero-gestation." By G. Rainey, Esq., M.R.C.S.E., Demonstrator 
of Anatoniy, St. Thomas's Hospital. Communicated by Joseph PI. 
Green, Esq., F.R.S. 

The author first refers to the discovery of the difference which 
exists between the two classes of muscles; the voluntary, or those 
with striped fibres, and the involuntarj-, or those with unstriped 
fibres. He then notices that the opinion which is entertained re- 
specting the round ligaments being composed of the unstriped variety 
of muscular fibre is incorrect, these organs consisting chiefly of the 
striped muscular fibre. 

In support of the accuracy of this assertion, the author alleges 
the following facts : — 

First, that the round ligament arises by three tendinous and fleshy 
fasciculi ; one, from the tendon of the internal oblique, near the 
symphysis pubis, a middle one from the superior column of the 
external abdominal ring, the third from the inferior column of the 
same : from these points the fibres pass backwards and outwards, 
and uniting form a rounded cord — the round ligament ; after which, 
traversing the broad ligament, they go to be inserted into the angle 
of the uterus. 

The striped fibres are principally situated in its centre, and extend 
from its origin to within an inch or two of the fundus uteri ; as they 
approach which, the fibres gradually lose the striated character and 
degenerate into fasciculi of granular fibres of the same kind as those 
of the Dartos muscle ; both these fibres presenting similar micro* 
scopic characters when acted upon by glycerine. 

The author then states that the round ligament does not pass 
through the external ring to be lost in the labia and mons veneris; 
and argues from the fact of their consisting mainly of striped fibres, 
&c., that their use cannot be merely mechanical or subservient to 
the process of utero-gestation, and therefore he concludes that its 

224 Royal Society, 

function must be connected in some nay with the process of copula- 

He also adverts to the necessity of examining the round ligament 
by the microscoj)e in glycerine in preference to any other fluid ; as 
tliis substance renders the cellular tissue mixed with the fibres more 
transparent Mitliout diminishing the distinctness of their character- 
istic markings. Tlie author next states his views on the changes 
which take ])lace in the uterus during utero-gestation, and observes, 
first, that tiiere is no similarity between the fibres of the round liga- 
ment and those of the unimpregnated uterus, the latter being made 
up of spindle-shaped nucleated fibres, contained in a matrix of 
exceedingly coherent granular matter; that these fibres are best 
examined in j)ortions uhieh have been broken up by needles, in 
preference to thin sections ; and that this tissue is well seen in the 
larger mammals, as in the Cow, &c. In the impregnated uterus 
the fibres are I'ound much increased in size and distinctness, but 
devoid of nuclei and comparatively loosely connected ; and the en- 
largement of these fibres is of itself sufficient to account for the 
increased volume of the gravid uterus, without supposing that a set 
of muscular fibres are formed in it de novo. 

Hence he reasons that the unimpregnated uterus consists probably 
of little more than an assemblage of embryonic nucleated fibres, in- 
active until the ovum is received into it, after which their develop- 
ment commences and continues simultaneously and progressively 
with that of the foetus; so that when this last has arrived at a state 
requiring to be expelled, the uterus has accpiired its greatest expulsory 
power. Lastly, the author observes, since the fully-developed fibres 
cannot return to their former embryonic condition, they necessarily 
become absorbed, and a new set of embryonic fibres are formed for 
the next ovum, so that each foetus is furnished with its own set of 
expulsory fibres; which view is in perfect accordance with the 
statements of Drs. Sharpey and Weber, with regard to the mem- 
brana decidua. 

April 18. — "On the Solution of Linear Differential Equations." 
By the Rev. Brice Bronwin; I\LA. Communicated by S. Hunter 
Christie, Esq., Sec. R.S. 

The methods employed in this paper to effect the solution or re- 
duction of linear differential equations consist of certain peculiar 
transformations, and each particular class of equations is transformed 
by a distinct process peculiarly its own. The reduction is effected 
by means of certain general theorems in the calculus of operations. 

The terms which form the first member of the first class of equa- 
tions are functions of the symbols is and r, the latter being a function 
of X, and the former a function of x and D, x being the independent 
variable. This member of the equations contains two arbitrary 
functions of w, and may therefore be of any order whatever. It 
likewise contains two simple factors, such for example as rar and 
'a;-\-nk, which factors are taken aw-ay by the transformation em- 
ployed, and consequently the equation is reduced an order lower; 
it is therefore integrated when of the second order. There is a se- 

Royal Society. 225 

ries of equations of this class, eacli essentially distinct from tlie rest, 
yet all reducible by a similar process. 

These equations contain two arbitrary functions of .r. The num- 
ber therefore of particular practicable forms, which may be deduced 
from each, is very great, a circumstance whicii renders our ciiance 
of putting any proposed equation under one of these forms greater 
in the same proi)ortion. On account of the very large number of 
particular integrable equations which each general example furnishes, 
selection would be very difficult, and all could not be given ; the au- 
thor has therefore refrained from giving any. 

The second class of equations may be deduced from the first by 
the interchange of the symbols D and a-, and changing r into r-^ 
The second general theorem can be deduced from the first in like 
manner; and this class may be transformed and reduced by it in a 
manner exactly similar to that by which the former class is reduced 
by the first general theorem. The solution therefore of the one se- 
ries may be deduced from that of the other by the interchange of 
symbols only. But in the second series the solutions obtained are 
not always practicable, that is to say, they cannot always be inter- 
preted in finite terms. They have therefore been reduced by the 
introduction of new arbitrary functions of D, which render them 
practicable ; this process however necessarily diminishes their gene- 

When reduced to the ordinary form, these equations are somewhat 
complicated ; but by giving suitable forms to the arbitrary functions 
of D which they contain, we may derive from them particular ex- 
amples of a form as simple as we please, and by introducing as many 
arbitrary constants as possible, these examples may be made very 
general of the class to which they belong. In the integration of 
linear equations, the coefficients of which are integer functions of x, 
they may prove very useful. 

Next, an equation, a particular case of which was treated by Mr. 
Boole in the Cambridge Mathematical Journal, is here integrated 
under its most general form. Instead of integer functions of a', the 
coefficients may be any functions whatever, consistent with the con- 
dition of integrability, which is ascertained, and the formulae of re- 
duction assumed by Mr. Boole are shown to be universally true. 
An additional function of the independent variable is also introduced 
into the operating symbol it. The equation therefore, independently 
of the condition of integrability, contains two arbitrary functions of 
X, and consequently gives rise to a considerable number of particular 
integrable examples. 

Here also the interchange of the symbols D and x is made, both 
in the equation to be integrated and in the general symbolical 
theorem Jjy which it is reduced, and the same reduction to prac- 
ticable forms as before is likewise made. 

The next class of equations results from the generalization of an-" 
other equation integrated by Mr. Boole in the Cambridge Mathema- 
tical Journal. Here the symbol D of Mr. Boole is replaced by the 
general symbol w, and moreover the first member of each equation 
contains two arbitrary functions of or ; and by means of another 

Phil. Mag, S. 3. Vol. 37. No. 249. Sept. 1 850. Q 

226 Royal Societt/. 

extension, this example gives rise to a whole series of equations con- 
stituting a class. Tiio reiliiction is ert'ccted jiartly by the first general 
theorem in the calculus of operations, and partly by other means. 
It must be observed that cacii of the classes is totally distinct from 
the others, and its mode of treatment also distinct; also each of the 
general examples in the series contains two arbitrary functions of the 
independent variable, and will therefore give the solutions of a large 
number of particular equations, but for the reason before stated 
particular examples are not given. 

Here likewise, by the interchange of the symbols D and x, another 
series of equations with their solutions or reductions is obtained, and 
also another general theorem by whicii tiiey may be transformed and 
reduced. But the solutions of the examples of the one series may 
be deduced from those of the other by the interchange of symbols. 
It is not a little remarkable that this interchange of symbols in all 
tliese cases should be found possible, it will however be found pos- 
sible in another case to be hereafter described. 

The last class of equations discussed in this paper is transformed 
by means of a general tiieorem of a very different kind from any of 
those which have been employed in reducing and integrating any of 
the previous classes. By means of this transformalion, the symbol 
vj, of which the first member of these equations is a function, is 
placed in a position to operate upon the whole of that member, a 
certain equation of condition among the coefficients being previously 
admitted. Hence by operating upon both members with the inverse 
of this symbol, the equation is once integrated, and, if it be of the 
second order only, completely solved. 

Here too the interchange of symbols may be made both in the 
equation and its solution, and the solution so changed will be the 
solution of the equation changed in like manner. The general sym- 
bolical theorems, which here consist of a series of terms, may be de- 
rived the one from the other in the same way, and by changing the 
signs of the alternate terms. 

Reductions of the arbitrary functions of D, similar to those before 
made, are made here also; and by particularizing some of the func- 
tions so reduced for the sake of simplification, several very singular 
resulting equations are obtained. If in these w-e assign to the re- 
maining arbitrary functions, particular forms, and introduce as many 
arbitrary constants as we can, we may find particular examples 
which may be of great use in the integration of equations with 
coefficients containing only integer functions of a;. 

By a very obvious suI)stitution an arbitrary function of x may be 
introduced into any of this kind of equations, and also another func- 
tion of D, and the last often with great advantage. 

" On the Oils produced by the Action of Sulphuric Acid upon 
various classes of Vegetables," by John Stenhousc, Esq., F.R.S. 

Nearly thirty years ago Ddbereiuer observed, when preparing for- 
mic acid by distilling a mixture of starch, peroxide of manganese and 
sulphuric acid, that the liquid which passed into the receiver con- 
tained a small quantity of oil which rendered it turbid. To this oil 
Dobereiner gave the fanciful name of " artificial oil of ants," though 

Royal Society. 227 

the very limited quantity in Avhich he was able to procure it pre- 
vented him from determining almost any of its properties. 

The author's attention Mas first directed to the subject in 1840, 
when he found tliat the oxide of manganese was unnecessary, and 
that the oil could be readily prepared by operating on most vege- 
table substances with either sulphuric or muriatic acid. The oil, on 
analj'sis, was found to have the formula Cj^ H^ Og, and to contain 
oxygen and hydrogen in the proportions to form water, while all 
otiier oils and fats contain an excess of hydrogen. 

The late Dr. Fownes took up the subject in IS^S, and made the 
interesting discover}', that when the oil which he called furfurole is 
heated with ammonia, a crystalline amide is formed. When this 
amide is boiled with caustic lyes, it is changed into the crystallizable 
base fui'furine. The paper then describes the best mode of pre- 
paring furfurole, and also the method of purifying it from an oil with 
which crude furfurole is always accompanied, and to which the name 
of meta-furfurole has been given. Meta-furfurole is the cause of the 
bright red coloration which impure furfurole instantly produces when 
it is treated with muriatic or sulphuric acids in the cold. This por- 
tion of the paper concludes with some new observations on furfurole, 
and an examination of some of the salts of furfnrine. 

It has been pretty satisfactorily ascertained that the constituent 
of plants which yields furfurole is the matiere incnistcmte of M. Payen, 
viz. the matter with which the interior of the cells of plants is lined. 
This is an amorphous granular substance which has been gradually 
deposited from the sap in its passage through the tissue of the plant. 
It is most abundant in hard woods, such as oak and teak, especially 
in the oldest portions which lie nearest the heart of the tree. As the 
author of the paper was led to conjecture that the matiere incrustante 
of the different gi'eat classes of vegetables would be found on exa- 
mination analogous but not identical, he thought it likely that the 
oils derivable from them would also prove not identical with furfurole, 
though probably very analogous to it in their nature and properties. 
The algas or sea-weeds, whose structure is very different from that 
of ordinary herbaceous plants, were employed to test the truth of this 
hypothesis. They yielded an aromatic oil to which the name of 
fucusole was given. Though' essentially different from furfurole, it 
closely resembles that oil in its proj^erties, being also isomeric with 
it. Fucusole forms a crystallizable amide with ammonia, called fucus 
amide, which, when it is boiled with alkaline lyes, is also converted 
into an organic base — fucusine, which is likewise isomeric with fur- 
furine. Fucusine is a rather difficultly crystallizable base; but some 
of its salts, especially the nitrate, may be readily procured in large 
crystals. In solubility and crystalline form they diffier fi'om those 
of the corresponding base. 

The paper contains an analysis of these salts. 

The mosses and lichens were also found to yield fucusole. The 
ferns, on the other hand, yield a peculiar oil, which differs both from 
fucusole and furfurole, possessing properties intermediate between 

The results of these experiments seem to indicate some curious 


228 Royal Society, 

botanical rolatidiis, as it a])i)i>ai> hij^lily ])robal)lo that the maticre 
iiicruskmte is tlio sanio in all ])han(>roganioiis plants, as they yield 
ruiTurolc. On tiie other hand, the t/Kidcrc iiicnistcode in tiie Algae, 
mosj^es and lichens, as it yields fucusole and not f'urfurole, thougli the 
same in each of these classes, is evidently different from that of pha- 
nerogamous plants. The matiere incrustante of ferns appears how- 
ever to be dissimilar from either of the others, as it yields an analo- 
gous but peculiar oil. 

April 25. — " On the means adopted in tiie British Colonial Mag- 
netic Observatorifs for determining the al)solute values, secular 
change, and annual variation of the Magnetic Force." By Lieut.-jCol. 
Edward Sabine, R.A., For. Sec. U.S.' 

The determination of the mean numerical values of the elements 
of terrestrial magnetism in direction and force at different points of 
the earth's surface (the force being expressed in absolute measure, 
intelligible consequently to future generations, however distant, and 
conveying to them a knowledge of the present magnetic state of the 
globe), and the determination of tiie nature and amount of the se- 
cular changes which the elements are at present undergoing, are, as 
the autlior states, tiie first steps in that great inductive inquiry by 
which it may be hoped that tlie inhabitants of the globe may at some 
date, perhaps not very distant, obtain a conqdete knowledge of the 
laws of tlie phenomena of terrestrial magnetism, and possibly gain 
an insiglit into the physical causes of one of the most remarkable 
forces by which our planet is affected. 

After stating the inadequacy of the instruments originally pro- 
posed by the Royal Society, to the attainment of all the objects for 
which they had been designed, the author refers to the modifications 
which had been introduced, in the instruments and methods of ob- 
servation for the determination of the absolute values, and the secu- 
lar changes of the horizontal component of the magnetic force. He 
then gives the series of the results of the monthly observations at 
Toronto from January IS^o to April 1849 as relatively correct ; and 
from this series, regarding each monthly determination as entitled 
to equal weight, and taking the arithmetical mean of all the values 
as the most probable mean value, obtains 3*53043 as the mean value 
of the horizontal force at Toronto, with a probable error of + '00055; 
and the probable error of +*0040 for each monthly determination. 

This is on the most simple hypothesis, in which neither secular 
change nor annual variation is supposed to exist. The monthly re- 
sults however distinctly indicate a secular change, and by means of 
them, on the hypothesis of a uniform secular change, the author 
deduces '0042 as the annual decrease of the horizontal force during 
the period comprehended by the observations, the value of the force 
on the 1st of ^Nlareh ISl'T, the mean epoch being S'SSO^S, with a 
jorobable error of +"00025. 

For the purpose of deducing the values of the total magnetic force 
and its secular change from those of the horizontal force, it is neces- 
sary to know the magnetic inclination corresponding to the epoch 
and its secular change. From the observations of the inclination, 
75° 16''09 is deduced as the value of this element on the 1st of March 

Royal Society, 2'29 

1847, with a secular increase of 0'*S9 annually; and 13*8832 as the 
value *ot" the total force in absolute measure, at the same epoch. As 
the annual increase of 0''89 in the inclination will not account for an 
annual decrease of more than '0033 in the horizontal force, there 
remains '0009 as indicative of a small annual decrease in the total 
force during the period of the observations, and the author considers 
that the probabilities are in favour of such a decrease- 

The general fact of an annual variation of the horizontal force at 
Toronto, the force beins; greater in the summer than in the winter 
months, is shown by three independent methods of experiment, viz. 
the observations from which the foregoing conclusions have been 
drawn, the regular observations with the bifilar magnetometer, and 
observations undertaken expressly with the view of ascertaining the 
fact. The author also infers the probable existence of an annual 
variation of the total force, the force being greatest in the winter 
months, or when the sun is in the southern signs, and least in the 
summer months, or when the sun is in the northern signs. 

The results obtained from the observations at Hobarton are next 
briefly stated. The investigation, conducted in the same manner as 
at Toronto, shows at Hobarton a decrease of soufk inclination of 
0'*89 on the average of the months from April to August inclusive, 
that is, in the southern winter ; and an increase of 0''85 from October 
to February inclusive, that is, in the southern summer. 

The series of observations on the horizontal force shows an annual 
variation of the same character as respects the seasons, and almost 
identical in amount with that at Toronto. In the months from 
October to February inclusive, or in the summer months at Ho- 
barton, the horizontal force is '001 7 greater on the average than its 
mean amount; and from April to August inclusive, or in the winter 
months at Hobarton, it is on the average '0013 less than its mean 

The inferences drawn from these variations of the inclination and 
horizontal force, taken jointly as respects the total force at Hobarton, 
are that this force is subject to an annual variation, being higher 
than its mean amount from October to February, and lower than its 
mean amount from April to August. 

It thus appears that in the months from October to February the 
magnetic needle more nearly approaches the vertical position, both 
at Toronto in the northern hemisphere, and at Hobarton in the 
southern ; and that the total force is greatest at both stations from 
October to February, and least from April to August. 

It is much to be desired, the author states, that so remarkable a 
result should receive a full confirmation, by the continuance of the 
observations at Toronto and Hobarton for such an additional period 
as may appear necessary for that purpose ; and that the general con- 
clusion, indicated by the observations at those stations, should be 
verified by similar investigations in other parts of the globe, especially 
at the observatories which now exist. He conceives that these facts 
indicate the existence of a general affection of the whole globe 
having an annual period, and would appear to conduct us naturally 
to the position of the earth in its orbit as the first step towards an 

230 Cambridge Philosophical Society. 

explanation of the periodic change. He further urges the importance 
of loilowing up without delay, and in the most effective manner, a 
brancli of the research wiiich gives so fair a promise of establishing, 
upon the basis of competent experiment, a conclusion of so much 
theoretical moment. 

In conclusion tlie author adverts briefl}' to considerations which 
may give a particular importance to accurate numerical values of the 
magnetic elements and their secular changes at Toronto, namely the 
proximity of that station to one of tlie two points on the northern 
hemisphere, wiiich are the centres of the isotiynamic loops, and are 
the points of the greatest intensity of the force (on the surface of 
the globe) of apparently two magnetic systems, distinguished from 
each other by the very remarkable difference in the rate of secular 
change to which the phenomena in each system appear to be subject. 


[Continued from p. 153.] 

March 11, 1850. — On the Knowledge of Body and Space. By 
H. Wedgwood, M.A. 

No ])art of the great metaphysical problem chalked out by Locke 
has been more assiduously laboured, and none has attained a less 
satisfactory solution, than that which relates to the origin of the 
idea of space and its subordinate conceptions, figure, position, mag- 

It was seen that the exercise of the muscular frame must somehow 
be instrumental in making us acquainted with the material and ex- 
tended world, but all hopes of a logical explanation of the process 
by which that effect is produced seemed cut off at the outset by a 
preliminary objection. The knowledge of motion, it was said, ob- 
viously involves the knowledge of the body moved. The conscious- 
ness of the motion of the hand therefore implies the conception of 
the hand itself, an object of certain shape and size. The attempt 
to account for the notions of shape and size from the motion of the 
hand was thus apparently stranded in a hopeless paralogism ; and so 
insurmountable was the difficulty taken to be, that philosophers were 
driven to imagine a second source of elementary ideas, in addition 
to the simple apprehension of the thing conceived in actual existence, 
maintaining that space is know'n to us as the condition under which 
we perceive external things, or, as others express it, that the notion 
of space arises in the mind on the first apprehension of body by a 
principle of necessary judgement, which impresses upon us the con- 
viction that all body is contained in space. 

In the paper laid before the Society, an attempt is made to show 
the utter barrenness of this hypothesis of a necessary origin (as it is 
called) of the idea of space ; and the main object of the paper is to 
rest the idea on a more solid foundation, by showing the adequacy 
of muscular exertion, in conjunction with the sense of touch, to fur- 
nish us w'ith complete knowledge of the material and extended world 
by the ordinary way of actual experience. 

There are two kinds of action ; one instinctive, immediately in- 

Cambridge Philosophical Socictij. 231 

duced by the pln'sical constitution of the agent independent of the 
vinderstandiu"^ ; the other rational, induced by the discernment of 
some object of desire in the end to be accomplished, and of course 
implying a previous conception of the action in question. 

Familiar instances of instinctive action are then pointed out, from 
whence it would appear that the sensations of touch felt on contact 
of any part of the living frame with a foreign body operate as motives 
to instinctive exertion through the instrumentality of that part of 
the muscular frame on which the sensible impression is made, in- 
stinctively impelling the sentient being to muscular reaction against 
the material cause of the sensation, or leading him to shrink from 
it if the sensation is of a painful nature. 

Attention is directed in particular to the action of an infant in- 
stinctively closing his hand upon a finger placed within his palm ; 
and it is argued that the effect of such an action on his understanding 
will be the direct apprehension of body, a complex object consisting 
of surface (undeveloped as yet in form and magnitude) apprehensible 
by tactual sensation ; and substance, revealed by resistance to mus- 
cular exertion, constituting a new kind of being essentially different 
from any of those discerned by means of the five senses. 

The relation between body and space is illustrated by comparison 
with the case of light and darkness, the second of the two correla- 
tives belonging in each case to Locke's class of positive ideas from 
negative causes. As he who has once apprehended light is subse- 
quently enabled to look for that phaenomenon in a direction from 
whence no rays actually penetrate the eye, so, it is argued, will he 
who has once made use of his hand in the apprehension of body be 
enabled to stretch out the same member in feeling for body when 
none is actually within reach ; and as in the former case the failure 
of the effort to discover light results in the sensible impression of 
black or darkness, so in the latter case the effort unsuccessfully 
aimed at the apprehension of body will take effect on the intelli- 
gence in the direct cognition or actual experience of space, viz. of 
that particular portion of space through which the hand, is moved in 
the unsuccessful search after body. 

Thus the notion of space,, like that of body, or of any sensible 
phsenoraenon, is traced to the actual experience of the thing itself 
in concrete existence. The subsequent enlargement of the idea, so 
as to comprehend the space occupied by the solid substance of bodies 
and that which stretches away to infinity in all directions around us, 
is duly accounted for on the same princi})le ; and that impossibility 
of conceiving the destruction of any portion of space, on which so 
much stress has been laid as establishing the necessity of a deeper- 
seated origin than simple experience, is shown to be the natural 
consequence of the negative foundation of the idea as explained ,by 
the analogy of light and darkness. 

May. 13. — Results* connected with the theory of the singular solu- 

* This communication is the abstract of a part of a paper not yet com- 
pleted, and was forwarded to the Society for the purpose of ascertaining 
whether any examples could be produced destructive of the perfect gene- 
raUty of the results. 

232 Cambridge Philosophical Society. 

tiou of a Differential Equation of the first order between two vari- 
ables. By Professor Do Morgan. 

By a singular solution of a differential equation is here meant any 
solution which can be obtained by differentiation only, w'hetheritbe 
a case of the primitive by integration or not. 

By a curve is meant all that is included under one equation, whether 
resoluble into what are commonly called complete curves or not. 
Thus, the equation 

(.t-y)(.t-> + y'^-l) = 

belongs to a curve, having a rectilinear branch and a circular one. 
By such a symbol as i',, is meant the partial differential coefficient 

— , when obtained from an equation in which v is explicitly expressed 

in terms of .r and (it may be) other variables. 

Let <p(.r, y, c') = be the complete primitive of the differential equa- 
tion y'=;^(.r,y). 

(p(x, 1/, c) belongs to two distinct classes of curves : — 

1. Continuous curves derived from such values of c, real or ima- 
ginary, as will enable <p = to exist for points infinitely near to one 

2. Systems of points, derived from 

A(.v,y,cc,l3)=:0, B(a-.y,a./3) = 0, 

^(.r, y, a-f /3 V-l) = A(a; y, a, /3) + B(a.', y, a, /3). v'- 1- 

When a curve is such that the points on one side of it are on 
cur\'es of the first kind, and those on the other side are part of 
systems of the second kind, let that curve be called a separator ; and 
the same when it separates points of both kinds from points which 
belong to one kind only. 

No solution of the differential equation can be formed by combining 
all those systems of the second kind in which a and /3 are connected 
by a real relation. 

The curve which has at every point of it, either 

^=00, ^ = 00, 
<Pc <Pc 


ri.= oo, ^ finite, ..r= const., 

i^= 00, ^ finite, i/ = const., 

<Pc fc 

is a singular solution. And in the above are contained all the sin- 
gular solutions. 

Every branch of a singular solution is either — 

A separator, only. 

A curve, every point of which has a contact of the first order at 
least with some one real primitive, only. Or both. Or neither. 

If the first or lastj it is a case of the complete primitive. And 

Cambridge Philosophical Society. 233 

such cases may be introduced at pleasure into the singular solution, 
by writing the primitive in the form 

A branch of a singular solution has at the utmost n contacts with 
each primitive which it touches {n being determined by the nature 
of the equation), and all of the lirst order, generally. Or, pi of the 
first order, jj.^ of the second, &c., p^-\•'2p.,-'rZp.^^\■ ... being « or n — 
(an even number) ; or some of these cases for some primitives, others 
for others, including the possibility of some cases giving none at all, 
when n is even. 

The branches of the singular solution which have contact with 
ordinary primitives (whether themselves ordinary primitives or not) 
to the exclusion of the branches which are only separators, may be 
determined from the differential equation by the following test. 

Let ?/' = %( J7,?/) be the differential equation; whence 

Find the curves which satisfy either of the following sets of con- 
ditions : — 

^ =: 00 ^ = <» y" finite, 


j^ = 00 A'= const, y" finite, 


-^ ■= cxi y= const, y" finite. 

Every such curve does satisfy the differential equation, and is a 
singtdar solution having contact with some one primitive at every 

And other such singular solutions there are none except those 
designated bv x^ co, or 3/= oo, or both. 

But if 

;^ = 00 and % = cc y"= 00, 


% = CO .r= const. y"= cc, 


p^ = CO y= const, y "= 00, 

then the differential equation may or may not be satisfied ; but the 
curve passes through the singular points of the primitives, with or 
without contact, according as the differential equation is or is not 
satisfied. An evolute is such a pseudo-singular solution to all the 
involutes, passing through their cusps. 

[ 23i ] 
XX\'III. IntclUgcuce arid Miscellaneous Articles. 


]\/r B. COKENWINDEIl remarks that the combniations of 
■^-^J- • iodine and jihosphorus have been hitherto unknown, means 
not having lieen found for obtaining them in a definite state and in the 
crystalline form. A method however exists of preparing these bodies 
crystallized. It consists in successively dissolving phosphorus and 
iodine in suljjhuret of carbon and cooling the solution. Crystals of 
iodide of i)hosphorus are soon deposited, the composition of which 
depends upon the quantities employed. 

In operating on two equivalents of iodine and one of phosphorus, 
M. Corenwinder obtained prismatic crystals of large dimensions, of 
an orange colour, and which by analysis gave the composition I-'Ph. 
This is the protiodide of phosphorus. It melts at 230° F., alters 
by exposure to the air, and volatilizes at a higher temperature. It 
may be advantageously employed for preparing hydriodic acid. 

By taking 3 equivalents of iodine and 1 of phosphorus and con- 
centrating the solution, irregular crystals of a deep reddish-brown 
colour are procured ; they have the appearance of hexagonal tables. 
This is the deutiodide of phosphorus; it melts at about 115° F., and 
decomposes by water, yielding hydriodic acid when heated with a 
small quantity of liquid. 

In operating on quantities in the proportions of 1 equivalent of 
phosphorus and 1 of iodine, crystals of protiodide are obtained, and 
excess of phosphorus remains in the liquid. 

With 5 equivalents of iodine and 2 of phosphorus, protiodide cry- 
stallizes first, and afterwards deutiodide, which gives the following 
equation: 5I + 2Ph = I-Ph + l3Ph. 

With 4 and 5 equivalents of iodine and 1 of phosphorus, iodine 
is at first deposited, then crystals of deutiodide, I Ph, 

By employing sulphuret of carbon as a solvent, M. Corenwinder 
was able to obtain several other compounds, as chloride of phos- 
phorus and sulphuret of phosphorus, &c., in crystals. — L'Institut, 
7 Aout, 1850. 


Tritomite. — This mineral was found in the island of Lamoe, near 
Brevig, in isolated crystals, disseminated in a coarse-grained syenite, 
and accompanied by leucophane, mosandate, catapleite, &c. 

The crystals are regular tetrahedrons, the faces of which are dull 
and covered with a reddish-brown crust ; the fracture is conchoidal, 
without cleavage, and the lustre is vitreous and metallic. This 
mineral is very harsh, its colour is a deep brown, and its powder is 
yellowish-grey ; it is opake or translucent only on the edges. Its 
hardness is between that of felspar and apatite, and its density is 
4-16 to 4-66. 

Before the blowpipe tritomite whitens, exfoliates, and splits. 

Intelligence and Miscellaneous Articles. 235 

sometimes flying into fragments. Heated in a tube it loses water, 
which acts as weak hydrofluoric acid. With borax it gives a glass 
of a reddish-brown colour, which decolorizes on cooling. Reduced 
to powder it is attacked by hydrochloric acid, with the evolution of 
chlorine, and the separation of gelatinous silica. 

M. Berlin obtained the following as the results of the analysis of 
this mineral, which, however, on account of the rarity of the mineral, 
are to be considered as merely approximative : — 

Silica 20-13 

Oxide of cerium 40'36 

— ^^ — of lantanium 15" 1 1 

Lime 5'15 

Alumina 2 24 

Yttria 0-46 

Magnesia 0"22 

Soda 1-46 

Protoxide of iron 1'83 

Manganese, co^jper, tin and tungsten. 4*62 
Loss by calcination 7'86 

From the analysis, this mineral appears to be a hydrated tribasic 
silicate of cerium, lantanium, and lime. 

Catapleite. — This mineral accompanies the preceding. It exists 
in imperfect crystals, consisting of a prism of about 1 20", terminated 
by an oblique base, also inclined at about 120°. Sometimes it 
exhibits indications of several vertical faces. Cleavage perfect ac- 
cording to the base. Fracture splintery. Dull or very little lustre, 
even when fractured. Colour light yellowish-brown, powder isa- 
bella-yellow ; op-ake or a little chatoyant. Hardness resembling 
that of felspar ; density 2-8. 

This mineral readily fuses into a white enamel ; it dissolves with 
difficulty in borax, forming a colourless glass. A solution of cobalt 
renders it blue. Reduced to powder it is readily decomposed by 
hydrochloric acid, but does not gelatinize. 

Its analysis gave M. Sjogren the following results : — 

I. II. 

Silica 46-83 46-52 

Zinconia 29-81 29-33 

Alumina 0-45 1-40 

Soda 10-83 10-06 

Lime 3-61 4-66 

Protoxide of iron . 0-63 0*49 

Water 8-86 9*05 

101-02 101-51 

Its composition may be represented by the formula — 

3 ^^Q \ SiOs + 2ZrO^ Si03 + 6Aq. 

236 Intelligence and Miscellaneous Articles. 

Atheriastite. — This mineral was long confounded with paranthinc; 
it is found in an abandoned iron mine at Naes, near Arendal, ac- 
companied with black garnet and kcilhauite in a granitic rock. 

Its primary form is an octohcdron with a square base, the adjacent 
faces of which form angles of about 135°; this octohcdron is accom- 
panied by two square prisms. Tlie crystals are short and thick, 
and the angles and edges are usually rounded. Cleaves readily 
according to the second square prism. Fracture uneven and splin- 
tery, dull or chatoyant. Colour pale green, powder greenish gray ; 

It swells before the blowpipe, and readily fuses into a deep brown 
glass. Hydrochloric acid attacks it very feebly. 

By M, Berlin's analysis it yielded — 

Silica 3800 

Alumina 24- 10 

Lime 2-2-64 

Magnesia 280 

Protoxide of iron 4*82 

Protoxide of manganese . . 0'78 

Water G-95 


If a part of the iron be supposed to be in the state of peroxide, 
this composition may be represented by the formula — 

2(3CaO, Si03) + 3Al2 03Si03-f4Aq. 

Eudnophite. — This mineral was found in the syenite of the island 
of Lamoe, with the two first minerals above described. Its crystals 
are very rare ; they are derived from a right rhombic prism, giving 
a prism of about 130°, terminated by a bevil, and truncated at the 
acute edges. Cleavage perfect according to the base ; there also 
exists a more difficult one according to the diagonal planes. Frac- 
ture even, slightly splintery. The faces are dull or a little brilliant, 
lustre slightly pearly when fractured. Colour white, passing to 
gray or brown ; powder white. Fragments translucent or trans- 
parent. Hardness between that of felspar and apatite. Density 2'27. 

Before the blowpipe this mineral fuses into a colourless glass. 
Reduced to powder, it is decomposed by hydrochloric acid with the 
formation of gelatinous silica. 

It has been analysed by M. de Bock (I.), and by M. Berlin (II.). 

(I.) (ir.) 

Silica 54-93 55-06 

Alumina 23-59 23-12 

Soda 14-06 14-06 

Water 8-29 8-16 

100-87 100-40 

These results agree exactly with the formula of analcime, 
3NaO, 2Si03+3(Al^ 03, 2Si03) + 6HO, and may seem to indicate 

Intelligejice and Miscellmieous Articles. 237 

that eudnophite is a dimorphous species of analcime. — Pogg. Ann. 
tome 79 ; Bibliotheque Univcrsclle, Juin 1850. 


Hyposklerite is a mineral of a felspathic appearance, which lias 
heen described by M. Brcithaupt. An analysis recently made by 
M. Hermann seems to separate it completely from the felspars. 
M. Raramelsberg has repeated the analysis with a specimen which 
he received from M. Breithaupt himself. He did not find in it any 
traces of cerium and lantanium indicated by M. Hermann, and his 
results agree exactly with the composition of an albite, mixed with 
about 5 per cent, of pyroxene, a supposition Avhich is supported by 
the deep blackish green colour interspersed through some parts of 
the hyposklerite. It appears therefore that this mineral should not 
constitute a distinct species. — Ibid. 


After the discovery of the existence of so important a substance 
as iodine in so many bodies, M. Lamy thought it might be in- 
teresting to state how he had ascertained its presence in the beet- 
root of the Grand Duchy of Baden. 

In November last AI. Lamy received from M. L. Lintz, chemist 
at the sugar manufactory of Waghausel in the Grand Duchy, a spe- 
cimen of beet-root potash for examination, thinking that it contained 

Some fragments were accordingly dissolved in distilled water and 
saturated with nitric or sulphuric acid ; the solution was of a yellow 
colour and exhaled the odour of iodine ; by the addition of solution 
of starch, it became of an intense blue colour, which disappeared by 
heat and reappeared on cooling. 

After frequently repeating this experiment, and being certain of 
the existence of an alkaline iodide in the potash of Waghausel, M. 
Lamy examined successively the various products of the manufacture 
of sugar of this locality, beginning with the saline matter, molasses, 
then taking the refined sugar, unrefined sugar, and cassettes, or 
beet-root cut into small parallelopipeds and dried. 

The saline matter was treated with hot water as long as it dis- 
solved anything; the aqueous solution was evaporated to dryness, and 
the residue treated with highly rectified alcohol, the solution being 
evaporated to dryness ; the residue was divided into two portions ; 
one of these was treated with sulphuric acid and solution of starch, 
and the other was tried "by M. Reynoso's process ; in both cases 
the existence of iodine was evident. 

The ash of the molasses w'as boiled in distilled water ; a portion 
of the filtered liquor, saturated with nitric or sulphuric acid, gave, 
like the potash, a fine blue colour on the addition of solution of 
starch ; another portion, on spontaneous evaporation, left a cry- 
stallized residue which was treated w^ith hot alcohol of 40 degrees 

238 lutelligetice and Miscellaneous Articles. 

to dissolve the iodide and separate the foreign salts insoluble in it. 
The alcoholic solution was evajjorated to drj'ness, and the residue 
treated with water yielded a solution which gave a deep blue colour 
with starch. This colour was very permanent, disappeared on being 
heated and reappeared on cooling. 

The same treatment was followed with sugar unrefined and refined, 
but they gave not the least trace of iodine ; the cossettes, on the 
contrary, contained this substance ; the experiment was several 
times repeated and always with the same result. 

The author examined the beet-root from a manufactory in the 
neighbourhood of ^'ersailles, but he discovered no trace of iodine in 
it. As the manufactory of Waghausel is of great extent, M. Lamy 
thinks it probable that all the beet-root used in it may not contain 
iodine, and as salts of iodine are not uncommon in the salt-springs 
of Germany, he inquires, without attempting to decide, whether 
the presence of iodine may not be derived from the assimilation of 
the salts of iodine. — Journ. de Pharm. et de Chun., Juillet, 1850. 


Professor Page, in the lectures which he is now delivering before 
the Smithsonian Institution, states that there is no longer any 
doubt of the application of this power as a substitute for steam. He 
exhibited the most imposing experiments ever witnessed in this 
branch of science. An immense bar of iron, weighing 160 lbs., was 
made to spring up by magnetic action, and to move rapidly up and 
down, dancing like a feather in the air, without any visible support. 
The force operating upon the bar he stated to average 300 lbs. 
through ten inches of its motion. He said he could raise this bar 
100 feet as readily as ten inches, and he expected no difficulty in 
doing the same with a bar weighing one ton, or a hundred tons. 
He could make a pile-driver, or a forge hammer, with great simplicity, 
and could make an engine with a stroke of six, twelve, twenty, or any 
number of feet. The most beautiful experiment we ever witnessed 
was the loud sound and brilliant flash from the gulvanic spark, when 
produced near a certain point in his great magnet. Each snap was 
as loud as a pistol ; and when he produced the same spark at a little 
distance from this point, it made no noise at all. This recent dis- 
covery is said to have a practical bearing upon the construction of 
an electro-magnetic engine. He then exhibited his engine of between 
four and five horse-power, operated by a battery contained within a 
space of three cubic feet. It looked very unlike a magnetic machine. 
It Avas a reciprocating engine of two feet stroke, and the whole en- 
gine and battery weighed about one ton. When the power was 
thrown on by the motion of a lever, the engine started off magnifi- 
cently, making 114 strokes per minute; though when it drove a 
circular saw, ten inches in diameter, sawing up boards an inch and 
a quarter thick into laths, the engine made but about 80 strokes per 
minute. The force operating upon this great cylinder throughout 
the whole motion of two feet w-as stated to be 600 lbs. when the 
engine was moving very slowly ; but he had not been able to ascer- 

Meteorological Observations. 239 

tain what the force \vas when the engine was running at a working 
speed, though it was considerably less. The most important and 
interesting point, however, is the expense of the power. Professor 
Page stated that he had reduced the cost so far that it was less than 
steam under many and most conditions, though not so low as the 
cheapest steam-engines. With all the imperfections of the engine, 
the consumption of 3 lbs. of zinc per day would produce one-horse 
power. The larger his engines, contrary to what has been known 
before, the greater the oeconomy. Professor Page was himself sur- 
prised at the result. There were yet practical difficulties to be over- 
come, the battery has yet to be improved, and it remains yet to try 
the experiment on a grander scale — to make a power of 100 horse, 
or more. — National Intelligencer (American paper). 


Chistvick, — July 1. Cloudy: clear. 2. Fine. S. Rain: cloudy and boisterous. 
4. Heavy rain. 5. Fine : clear. 6. Fine : overcast. 7. Rain. 8. Very 
fine. 9. Cloudy: showery. 10,11. Very fine. 12. Fogjjy : overcast. 13, 
14. Overcast and fine. 15. Very fine: sultry: clear. 16. Very fine: cloudy. 
17. Slight haze: very fine : overcast : rain. 18. Heavy rain: sultry : cloudy and 
mild. 19. Rain. 20. Overcast. 21. Cloudy and fine. 22, S3. Very tine. 
• 24. Cloudy : rain at night. 25. Heavy showers. 26. Fine : windv : cloudy : 
rain. 27. Rain : showery. 28. Slight showers. 29. Cloudy: very fine : quite 
clear. 30. Cloudy : clear at night. 31. Slight haze : fine. 

Mean temperature of the month 61°'91 

IVIean temperature of July 1849 62 -29 

JVI can temperature of July for the last twenty- three years . 63 "23 

Average amount of rain in July 2'38 inches. 

Boston. — July 1. Cloudy: rain 2. Fine. 3. Cloudy. 4. Cloudy : rain 
with thunder and lightning p.m. 5. Cloudy. 6. Cloudy : rain a.m. and p.m. 
7. Rain. 8. Fine. 9. Cloudy: rain p.m. 10—12. Cloudy. 13 — 15. Fine. 
16. Fine: rain a.m. and p.m. 17. Fine. 18. Calm: rain p.m. 19. Rain: 
rain A.. M. and P.M. 20, 21. Cloudy. 22,23. Fine. 24. Cloudy : rain early a.m. 
25, 26. Cloudy : rain a.m. and p.m. 27. Rain : rain a.m. and 28. Cloudy : 
rain a.m and p.m. 29, 30. Cloudy. 31. P'ine : rain a.m. and p.m. 

Apiilegartli Alanse, Dumfries-shire. — July I. Heavy rain at night: showers. 
2. Showers all day and wind. 3. Showers: fair p.m.: wind. 4. Showers: 
cleared P.M. 5. Heavy showers : fine p.m. 6. Rain all day. 7, Fine a.m. : a 
few drops P.M. 8. Very fine all day. 9. Showers nearly all day. 10. Very fine 
all day. 11. Very warm : slight drizzle. 12. Very warm : thunder. 13. Very 
warm : oppressive. 14. Very warm : close. 15. Very warm : bright. 16. Very 
warm : slight showers : thunder. 17. Very warm : thunder. 18. Warm: dull: 
hazy: thunder. 19. Warm: shower early. 20. Waim still and pleasant. 21. 
Warm and fine: cloudy p.m. 22. Warm : a few drops of rain. 23. Warm : 
sultry: thunder. 24. Heavy rain. 25. FairA.ji. : wet all rest of the day. 26. 
Showery all day. 27. Very slight drizzle. 28. Fair : warm. 29. Fair and very 
fine. 30. Fair and warm. 31. Shower early : fair p.m. 

IVIean temperature of the month 59°"4 

INIean temperature of July 1849 57 '0 

Jlean temperature of .July for the last twenty-eight years ... 58 '1 

Average rain in July for twenty years 3'91 inches. 

Sandwick Afansc, Orkiu'i/. — July 1. Showers. 2. Clear : drops. 3. Rain. 4. 
Fine: clear. 5. Cloudy : clear. C. Clear: fine. 7. Clear: showers. 8. Showers: 
hail. 9. Bright : clear. 10. Cloudy : fine. 11. Fog: rain. 12. Cloudy. 13. 
Cloudy: fine. 14, 15. Fine: very fine. 16. Fine: very fine: hot. 17. Drops: 
showers: fog. 18. Cloudy: fine. 19. Cloudy : fine : cloudy. 20. Cloudy: 
fine: fog. 21. Bright : hazy. 22. Hazy : fine. 23. Bright: "fine. 24. Clear: 
fine. 25. Clear: fine: hot : fog. 26. Cloudy : hot : drizzle. 27. Fog : damp. 
28. Cloudy : fog. 29,30. Cloudy. 31. Bright: clear. 

I -saiAjuina 











■uid I 

O a 









: : c< CO : o cp : — : ; : : : o 9 <p ro o ; : : 7- 7* 

• i . • sT 8 ... 

ft w > fc c ^ ^ fe I -S aJ fc S S « S fe i <u <u " flJ S (J 

fe .-• s? fc 5^ ' te !»* h! .^" b.' .i .• . nJ Si I -i ft S> > ai ol iJ 

oJ C 5 

" e c 

^' « «• ft" 

° ft . 

^ fc 3s* ^ S:' :• i ft' ft* ft" ft « i oJ S' 

^ '. 

ft fe ft 

tn > t/i 

i i i ii^i i c c i 

C ^ 0^ C 

Q> ^ CA C ^ 

. S ft 

ft ft ft c ft' ft' ^ I o 0; ^ aJ ^ c ^' ft" c5 ^ CO ^' «• «• i ft* d S" g ft" 

— --t^— o— ^o*ot~c^■^^^ooo(^'<NlO•>*^o^o^^r^ooc^'^^r^<N'^^~Ol^ 


6^<^llO— O<^^00^OO^m^0t^OO^<OOO^00OlOt^^^O--c^6^t~-Q0M^O^O 

^OC^MTJ■Ococ'5 0^— cot^ooa^•^Ot>rJ'0^'*^ooc■lOO^O^■^■^<^I■^<M 

o — nooo — cooor^o^OQO^n■^^no^o^ot^^ooOlOoovoloa^MlOcs•>*oo 

!^^0^0^CT^6^0 O^C^a^C C>0 O O O O c^6^6^0^C^6^0 6^0^6^0^O O O O 

lOipT" ipc^ONCp OM3>o^c^p o o o o^qpaoopccooQOQp r^l>•lp^^o^■^ 7" p 


o 00 -^ in 
I c^ 10 o^ lO 

— CO 

00 — 
00 o\ 

— — ^r 
0^0^ — 

— 10 O >o 
iC lO 'S" — 

— Ol o c 

•^00 in 

6 6 6 


"l" — oo" 
o a^ o 
00 — 

moo <o 
— o <N 

O p CTi 

6 6 6> 

CO CO c» 

10 CO -^ 
o 10 t^ 

9 9 9^ 
6 6 c> 


00 o> 
00 -^ 
00 00 

01 o» 

CO 00 

o 10 • 

CTiOO ( 


— CTi 
— ' O 

CO -< 

T o 

en 00 

O (N 
C< CM 

in CO 

<N — 


ys o^ ■^ 

10 CN O 
O t^ CS 

10 o *o 

U3 UO O 
O — — 

■O I:^C^ < 
— o 00 < 
t^oo c^- 


<=■ s- 






[TinilD SERIES.] 

OCTOBER 1850. 

XXIX. Remarks on the Forces experienced by inductively 
Magnetized Ferromagnetic or Diamagnetic Non-crystaUinc 
Substances. By William Thomson, Professor of' Natural 
Philosophy in the University of Glasgoxv *. 

THE remarkable law laid down by Faraday in his Me- 
moir on the Magnetic Condition of all Matter, that a 
small portion oj' diamagnetic matter jjlaced i?i the 7icighbourhood 
of a magnet experiences a pressure urging it from places of 
stronger towards places of "jceakcr force, is a simple conclusion, 
derived from the mathematical solution of the problem of de- 
termining the action experienced by a small sphere of matter 
magnetized inductively, and acted upon in virtue of its induced 
magnetism. Without entering upon the analytical investigation, 
which will be found in a paper " On the Forces experienced 
by small Spheres under Magnetic Influence; and on some of 
the Phsenomena presented by Diamagnetic Substances f/' I 
shall, in the present communication, state and explain briefly 
the result, and point out some remarkable inferences which 
may be drawn from it. 

1. Let P be any point in the neighbourhood of a magnet, and 
let P' be a point at an infinitely small distance, which may be 
denoted by a, from P. Let R denote the force which a " unit 
north pole J" if placed at P would experience, or, as it is 

* Commiinicaied by the Author. 

t Cambridge and DubHii Mathematical Journal, May 1847. 

J That is, the end of an infinitely thin uniformly and longitudinally 
magnetized bar of " unit strength," which is repelled on the iv/wlc from the 
north by the magnetism of the earth; " unit strength " being defined by 
the following statement : — 

If two infinitely thin bars be equally, and each uniformly and longitu- 

Phil. Mag. S. 3. Vol. 37. No. 250. Oct. 1 850. H 

242 Prof. Thomson on the Forces experienced by inductively 

called, " the resultant magnetic force at P;" and let R' denote 
the same with reference to P'. Then, if a small sphere of any 
kind of non-crystalline homogeneous matter, naturally un- 
magnetic, but susceptible of magnetization by influence, be 
placed at P, it will experience a force of which the component 
along PP' is 

1 R'2-R2 

'^ 2 « ' 

where o- denotes the volume of the sphere, and \x, a coefficient 
depending on the nature of the substance. This coefficient, jot, 

has a value a httle less than — for soft iron, and it has very 

small positive values for all ferromagnetic substances con- 
taining little or no iron. 

2. If it be true, as I think it must be, that the forces experi- 
enced by diamagnetic substances are occasioned by the influ- 
encing magnet magnetizing them inductively*, and acting 
upon them fvhen so magnetized, according to the established 
laws of the mutual action of two magnets, the preceding re- 
sult will hold for all non-crystalline matter; and to apply it 
to a diamagnetic substance it will be only necessary to give jw. 
a negative value. 

3. To interpret this result, we may remark, that, by the ele- 
mentary principles of the differential calculus as applied to the 
variation of a quantity depending on the position of a point in 

space, it may be shown that the fraction is greater 

when the point P' is chosen in a certain determinate direction 
from P than in any other; that it is of equal absolute value, 
but negative, if P be chosen in the opposite direction ; and 

dinally, magnetized, and if, when an end of one is placed at a unit (an 
inch, for example) of distance from an end of the other, the mutual force 
between these ends is unity; the magnetic strength of each is unity. The 
force R, defined in the text, is of course equal and opposite to the force 
that a " unit south pole " would experience if placed at K 

* This most natural explanation of the pha^nomena which he had dis- 
covered is suggested by Faraday in his original paper on the subject, and 
it is confirmed by the researches of subsequent experimenters, especially 
those of Reich and Weber, who have made experiments to show that a 
diamagnetic substance, under the influence of two magnets, will act upon 
one in virtue of the magnetization which it experiences from the other. 
The extreme feebleness of the polarity induced in diamagnetic substances 
is proved by Faraday in a series of experiments forming the subject of his 
last communication to the Royal Society; in which an attempt is made, 
by very delicate means, to test the induced current in a helix due to mag- 
netization or demagnetization of a diamagnetic substance which it sur- 
rounds, but only negative results are obtained. 

Magnetized Non-crystalline Substances. 24^3 

that it vanishes if P' be in a plane through P at right angles 
to the line of those two directions. Hence it follows that the 
resultant force upon the small sphere is along that line, in one 
direction or the other, according as y. is positive or negative, 
and accordingly we draw the following conclusions: — 

(1.) A small ferromagnetic sphere, in the neighbourhood of 
a magnet, will experience a force urging it iii that direction in 
isohich the " magnetic force " increases most rapidly. 

(2.) A small diamagnetic sphere, in the neighbourhood of a 
magnet, will experience a force urging it in that directiofi in 
'which the niagtietic force decreases inost rapidly. 

(3.) The absolute magnitude of the force in any case in which 
the distribution of magnetic force in the neighbourhood of the 
magnet is known, is the value which the expression m § 1 ob- 

R'^ — R^ 

tains when we give the value found by means of the 

differential calculus, for a point P' at an infinitely small di- 
stance PP' in the direction of the most rapid variation of the 
magnetic force from P, the actual position of the ball. 

4. It is deserving of special remark, that the direction of the 
force experienced by the ball has no relation to the direction 
of the lines of magnetic force through the position in which it 
is placed. The mathematical investigation thus affords full 
confirmation and explanation of the very remarkable observa- 
tion made by Faraday (§ 24 1 8), that a small sphere or cube 
of inductively magnetized substance is in some cases " urged 
along, and in others obliquely or directly across the lines of 
magnetic force." It is in fact very easy to imagine, or actu- 
ally to construct, arrangements in which the resultant force 
experienced by a ball of soft iron, or of some diamagnetic 
substance, is perpendicular to the lines of the magnetizing 
force. For instance, if a ball of soft iron be placed symme- 
trically with respect to the two poles of a horseshoe magnet, 
and at some distance from the line joining them, it will be 
urged towards this line, in a direction perpendicular to it, 
and consequently perpendicular to the lines of magnetizing 
force in the space in which it is situated ; and a ball of bis- 
muth, or of any other diamagnetic substance, similarly situated, 
would experience a force in the contrary direction. Or again, 
if a ball of aiiy substance be placed in the neighbourhood of 
a long straight galvanic wire, it will be urged towards or from 
the wire (according as the substance is ferromagnetic or dia- 
magnetic) in a line at right angles to it, and consequently 
cutting perpendicularly the lines of force, which are circles with 
their centres in the wire and in planes perpendicular to it. 
5. The preceding conclusions enable us to define clearly the 


2 1 i Pi-of. Thomson on the Forces experienced by inductively 

sense in which the terms " attraction " and " repulsion " may 
be aj^plietl to the action exerted by a magnet on a ferromag- 
netic and a dianiagnetic body respectively. A small sphere 
of ferromagnetic substance, placed in the neighbourhood of 
a magnet, experiences in general, a force ; but the term attrac- 
tion^ according to its derivation, means &. force towards', and 
if we apply it in any case, we must be able to supply an ob- 
ject for the preposition. Now, in this case the force is towards 
places of stronger "magnetic force;" and hence the action 
experienced by a ferromagnetic ball may be called an attrac- 
tion if we understand towards 2)[aces of stronger force. Places 
of stronger force are generally nearer the magnet than places 
of weaker force, and hence small pieces of soft iron are ge- 
nerally urged, on the whole, towards a magnet (in consequence 
of which no doubt the term "attraction" came originally to 
be applied) : but, as will be seen below, this is by no means 
universally the case ; balls of soft iron being, in some cases, 
actually repelled from the influencing magnet; and the term 
"attraction" can only be universally used with reference to 
ferromagnetic substances, on the understanding that it is 
towards places of stronger force. The term " repulsion," the 
reverse of " attraction," may, according to the same princi- 
ples, be applied universally to indicate the force with which a 
small diamagnetic sphere is urged towards places of weaker 
force, or repelled from places of stronger force, 

6. The following passage, containing a statement of principles 
on some of which Faraday himself lays much stress, but which 
have not I think been sufficiently attended to by subsequent 
experimenters, is quoted from the article in the Mathematical 
Journal already referred to. 

7. "The result obtained above affords the true explanation 
of the phaenomenon observed by Faraday, that a thin bar or 
needle of a diamagnetic substance, when suspended between 
the poles of a magnet, assumes a position across the line 
joining them. For such a needle has no tendency to arrange 
itself across the lines of magnetic force ; but, as will be 
shown in a future paper, if it be very small compared with 
the dimensions and distance of the magnet (as is the case, 
for instance, with a bar of any ordinary dimensions, subject 
only to the earth's influence), the direction it will assume, 
when allowed to turn freely about its centre of gravity, will 
be that of the lines of force, whether the material of which 
it consists be diamagnetic, or magnetic matter such as soft 
iron : but Faraday's result is due to the rapid decrease of 
magnetic intensity round the poles of the magnet, and to the 
length of the needle, which is considerable compared with the 

Magyietized Non-cri/stalli?ie Substances. 2i5 

distance between the poles of the magnet ; and is thus ex- 
plained by the discoverer himself. (§ 2269) ' The cause of 
the pointing of the bar, or any oblong arrangement of the 
heavy glass, is now evident. It is merely a result of the ten- 
dency of the particles to move outwards, or into the positions 
of weakest magnetic action. * The joint exertion of the action 
of all the particles brings the mass into the position which, by 
experiment, is found to belong to it.' " 

8. It may be added to this, that the tendency of a bar, 
whether of ferromagnetic or of diamagnetic substance, in a 
uniform field of magnetic force, to take the direction of the 
lines offeree, depends on the effect of the mutual action of the 
parts in altering the general magnetization of the bar, and is 
consequently so excessively feeble for any known diamagnetic 
substance that the most delicate experiments woulil in all pro- 
bability fail to render it sensiblef . 

9. Faraday's law, stated at the commencement of these re- 
marks, may be illustrated by some very curious although 
extremely simple experiments, which I shall now describe 
briefly $. 

10. The special apparatus required is merely a long light 
arm (I have used one about four feet in height; but a much 
shorter rod, if suspended by a finer or by a longer torsion- 
thread, would have answered equally well) suspended from a 
" torsion-head " by means of a very fine wire, or thread of 
unspun silk fibres attached to it near its middle; and a case 
round it adapted to prevent currents of air from disturbing its 
equilibrium, but allowing it sufficient angular motion in a ho- 
rizontal plane. A small ball of soft iron is attached to one 
end of the arm (or hung from it by a fine thread, which, for 
the sake of stability in many of the experiments, as for in- 
stance, experiments 2 and 3 described below, must not be too 
long), and a counterbalance is adjusted near the other end so 
as to make the arm horizontal. If only a small angular mo- 
tion be allowed to the arm, the path of the ball will be sen- 
sibly straight, and we may consider that, by the arrangement 

* ' The extreme feebleness of the diamagnetic action, on account of 
which any small sphere or cube of the matter will experience very nearly 
the same force as if all the rest were removed, seems fully to justify this 

f A very brief communication on this subject was laid before the British 
Association at the meeting of 1848, and is pubiisfhed in the Report for chat 
year, under the title " On the Equilibrium of Magnetic or Diamagnetic 
Bodies of any form, under the Influence of Terrestrial Magnetic Force." 

:J: These experiments were shown, in illustration of lectures on magnet- 
ism in the Natural Philosophy Class in the University of Glasgow, during 
the Session 1848-49. 

246 Prof. Thomson o)i the Forces experienced by inductively 

which has been described, the ball is allowed to move with great 
freedom in a straight line, but prevented from all other motion. 

11. In making the experiments described below, it is con- 
venient to have two stops so arranged that the motion of the 
arm may be kept within any tlesired limits, and manageable 
in such a way, that by means of them the arm may be rapidly 
brought to rest in any position. In general, before com- 
mencing an experiment, the arm ought to be brought to rest 
near one end of its course, and kept pressing very slightly 
upon one of the stops by the torsion of the wire, which may 
be suitably adjusted by the torsion-head, and the other stop 
ought to be pushed away, so as to leave the arm free to move 
in one direction. 

12. Experiment 1. — Place a common bar-magnet with either 
pole, the south, for instance, near the ball of soft iron in its 
line of motion, but on that side towards which it is prevented 
from moving by the stop. Taking another bar-magnet of 
considerably greater strength than the former, bring its north 
pole gradually near the fixed south pole of the other, in the 
continuation of the line of motion of the iron ball. When 
this north pole reaches a certain position the arm will cease 
to press on the stop, and if we push the north pole a little 
nearer still, the arm will altogether leave the stop and take a 
position of equilibrium, in which, after it is steadied (as may 
easily be done by means of the stops), it will remain stable, 
although the stops be removed entirely. If, by means of one 
of the stops, the ball be pushed to any distance farther from 
the magnets than this position of stable equilibrium, it will 
return towards it when left free. If it be drawn a little nearer 
by means of the other stop, and, when left for a few seconds, 
it be found to continue pressing upon the stop, then, when 
the stop is removed, the ball will return to that position of 
stable equilibrium. If, however, it be very slowly drawn still 
nearer the magnets, when it reaches a certain position it will 
cease to press on the stop; and if after this it experience the 
slightest agitation, or if it be drawn any nearer, it will leave 
the stop and move up till it strikes the nearer magnet, in con- 
tact with which it will almost immediately come to rest. It 
thus appears that there is a position of unstable equilibrium 
for the ball between the former stable position and the nearer 
magnet. It is easy to arrange the torsion-head so that the 
torsion of the suspending-thread or wire may have as little 
effect as we please, by finding, by successive trials, either of 
these positions of equilibrium, subject to the condition that, 
when the magnets are removed, the torsion would not sensi- 
bly disturb the arm from the position so found. 

Magnetized Non-crj/stalline Substances, 24-7 

13. After the explanations which have been given above, it 
is scarcely necessary to point out that the position of unstable 
equilibrium, deterniined in this experiment, is a point where 
the magnetizing force due to the south pole is destroyed by 
that of the more distant but more powerful north pole; and 
that the position of stable equilibrium is one where the excess 
of the magnetizing force due to the north pole, above that 
which is due to the less powerful south pole, has a maximum 
value with reference to points in the continuation, through the 
less powerful pole, of the line joining the two poles. If the 
poles were mathematical points, and the bars so long that their 
remote ends could produce no sensible action on the ball, the 
position of unstable equilibrium would of course be such that 
its distances from the two poles voozdd be direct!// as the square 
roots of the strengths of the magnets; and, by the solution of a 
most simple " maximum problem," it may be shown that the 
stable position would be such that its distances from the poles 
"iSJOtdd be directly as the cidie roots of the strengths. 

14. Experiment 2. — Place two equal bar-magnets symmetri- 
cally with reference to the line of motion, with similar poles 
at equal distances on two sides, in a perpendicular to this line, 
and, to make the best arrangement, let the lengths of the 
magnets be in the continuations of the lines joining their poles. 
Operating by means of the stops, in a manner similar to that 
described for the preceding experiment, it is readily ascer- 
tained that there are two positions of stable equilibrium for 
the ball at equal distances on two sides of the line joining the 
poles, and that the middle point of this line is a position of 
unstable equilibrium. 

15. Here, again, the explanation is obvious. The positions 
of stable equilibrium being such that, with reference to points 
in the line of motion of the ball, the magnetizing force due 
to the two similar poles may be a maximum, are readily found 

to be at distances on the two sides of the line joining the 

poles (the length of this line being denoted by «), if these be 
mathematical points, and if the lengths of the bars be so great 
that the distant poles produce no sensible eflfects. 

16. Experiment 3. — Hold a common horseshoe-magnet with 
the line joining its poles perpendicular to the line of motion, 
of the ball, and, by a suitable management of the stops and 
of the torsion-head, the existence of a force urging the ball 
perpendicularly across the "lines of force" towards the mid- 
dle point of the line joining the poles, may be easily made 

17. Experiments on diamagnetic substances^ and onferro- 

24-8 Prof. Tlionison on the Forces experienced by inductively 

magnetic substances of feeble inductive capacity. — The pbaeno- 
niena discovered by Faraday relative to the action of magnets 
on substances not previously known to be susceptible of" mag- 
netic influence may be exhibited with great ease by means of 
the apparatus described above. Hmall balls of the substances 
to be experimented upon may be hung from one end of the 
-balance (the ball of soft iron being of course removed) by fine 
threads of sufficient length to allow the arm, which may be of 
any substance containing no iron, to be out of reach of any 
sensible influence from the magnet employed. There is in these 
cases no difficulty, regarding the length of the sus]ien(ling- 
thread, of the kind noticed above with reference to soft iron, 
as the magnetic forces experienced are never strong enough 
to produce lateral instability (that is, a want of stability in the 
line of motion), even with the lightest of the substances ex- 
perimented on, unless the suspending thread be far longer 
than is necessary. In the experiments I have made, tiie 
threads bearing the small balls have not been more than 
four or five inches lono;. The diameters of the balls have 
been from a quarter of an inch to an inch, or an inch and 
a half. Instead of simple bar-magnets of steel, which are 
not powerful enough to be convenient for these experiments, 
I have used a bar electro-magnet of very moderate power, 
consisting of a helix and soft iron core. This core is a cylin- 
der of about an inch in diameter and a foot and a half long, 
"joith round ends (nearly hemispherical), which, when the core 
is in its central position, extend about an inch beyond the 
helix on each side. By these means the repulsion of balls of 
diamagnetic substance, and the attraction of very feebly ferro- 
magnetic substances, may be shown with great facility. 

18. For example, I may mention that 1 have hung a small 
apple, whole, by a thread three or four inches long, and 
putting it at first at rest, pressing slightly (in virtue of torsion 
produced by the torsion head mentioned above) upon one end 
of the soft iron core previously to the excitement of the elec- 
tro-magnet, I have found that as soon as the galvanic current 
is produced, the apple is repelled away ; and, by pushing for- 
ward the soft iron core, I have chased it across the field 
through a space of four or five inches. 

] 9. I have also used the same apparatus to show that a body 
which is feebly attracted in air is repelled when immersed 
below the surface of a sufficiently strong solution of sulphate 
of iron in a small trough, so arranged that when, by the force 
of torsion, the body immei'sed in the liquid is made to 
press on a side of the trough, the electro-magnet may be 
placed with one end of its core pressing on the outside ol the 

Magnetized Non-crystalline Substances. 249 

trough, close to the point where it is pressed upon by the 
body within. Using small glass balls (wliich, when empty, 
exhibit no sensible effects of the influence of the' magnet), the 
magnetic conditions of different liquids filling them maybe 
easily tested. Faraday's beautiful experiments on the rela- 
tive magnetic capacities of solutions of sulphate of iron of dif- 
ferent strengths, or rather, other experiments to illustrate the 
same principles, may be performed in an extremely convenient 
manner, by filling a glass ball of this kind with a solution, 
hanging it from x)ne end of the arm, and, by a suitable ad- 
justment of the weight at the other, immersing it below the 
surface of another solution contained in the trough. I have 
found that whenever the difference of the strengths of the two 
solutions was considerable, the ball immersed was attracted 
or repelled by the external magnet, according as the solution 
contained in the ball was stronger or weaker than the sola- 
tion surrounding it. 

On the stability of small inductively magnetized bodies 
in positions of equilibrium, 
20. In the paper published in the Mathematical Journal 
(referred to above), I pointed out that a small ball of either 
ferromagnetic or diamagnetic substance placed in the neigh- 
bourhood of a magnet, and not acted upon by any non-mag- 
netic force, is in equilibrium if it be in a situation where the 
" resultant force " (that which was denoted by R) is either a 
maximum or minimum, or " stationary" in value; that a dia- 
magnetic ball is in stable equilibrium if, and not in stable 
equilibrium unless, it be situated where the force 11 is a mini- 
mum in absolute value; and that " if there be any point 
external to the magnet, at which the resultant force has a 
maximum value, it would be a position of stable equilibrium 
for a small bar of soft iron, and any other position is essen- 
tially unstable." Shortly after the publication of that paper, 
I succeeded in proving that the resultant force cannot be an 
absolute maximum at any point external to a magnet, and 
consequently that no position of stable equilibrium for a ferro- 
magnetic ball, perfectly free from all constraint, can exist. I 
have very recently found that there may be points where the 
resultant force is an absolute minimum without being zero;- 
and therefore there may be positions of stable equilibrium for 
a diamagnetic ball not included in the case of the force va- 
nishing, noticed in the previous paper. This case however 
affords the simplest illustration that can be given of that most 
extraordinary fact, that a solid body may be repelled by a 
magnet, or magnets, into a position of stable equilibrium. If, 

2.50 Prof. Thomson oti the Forces exjierienced hy indicctively 

lor instance, we take the arrani^ement (described for Exp. 2 
above) of two bar-mafrnets, fixed with similar poles near one 
another, we have obviously between these poles a point where 
the resultant force vanishes, and towards which consequently 
a small diamagnelic ball placed anywhere sufficiently near it 
would be repelled. It is easily shown that, actually under 
the action of gravity, a ball of diamagnetic substance would 
be in stable equilibrium a little below this position, without 
any external suj)port or constraint whatever, if only the 
magnets were strong enough. It is, however, extremely im- 
probable that any attempt to realize this by experiment will 
succeed, since, even in the most favourable cases, no diamag- 
netic repulsion upon a solid has yet been obtained which at 
all approaches in magnitude to the weight of the body. Still 
we must consider that a true theoretical solution of the cele- 
brated physical problem * suggested by " Mahomet's cofiin " 
has been obtained, which is not the least curious among the 
remarkable consequences of Faraday's magnetic discoveries. 

On the relations of Ferromagnetic and Diamagnetic Magneti- 
zation to the Magnetizing Force. 

21. In the mathematical investigation by which the result 
stated above was obtained, it is assumed that the magnetization 
of the substance of the ball in each case is proportional to the 
magnetizing force (although this assumption may of course be 
avoided by merely supposing //, to have a value varying with 
the force, which will not affect either the investigation or the 
form of the result). It appears to me very probable that this 
assumption is correct /or all known diamagnetic substances, and 
for ho?nogeneous feebly ferromagnetic substances ; since it is 
equivalent to an assumption that inductive magnetization of 
a substance does not impair or in any way alter its suscepti- 
bility for fresh magnetization by means of another magnet 
brought into its neighbourhood. This opinion cannot how- 
ever at present be regarded but as a mere conjecture, being 
as yet unsupported by experiment. It is indeed directly op- 

* It is I believe often thought that this problem is solved in the expe- 
riment in which a needle is attracted into a galvanic helix held with its 
axis vertical ; but I have convinced mjself that the needle always touches 
somewhere on the sides of the tube fif there be one round it) or on the 
wire of the helix : and I have also ascertained that, when a powerful helix 
is used with, in place of the needle, a tin-plate cylinder, even if it be very 
little less in diameter than the inner cylindrical surface of the helix, there 
is never stable equilibrium without contact between them, Thephaenomenon 
of a solid body, hovering freely in the air, in stable equilibrium, without 
any external support or constraint, has never, I am convinced, been wit- 
nessed as the result of any electrical or majuetical experiment. 

Magnetized Non-cri/stalline Substances. 251 

posed to the following conclusion to which M. Pliicker arrives, 
from some of his experimental researches : — "J'ai dediiit de 
la cette loi generale, savoir: que le diamagnetisme ducroit 
plus vite que le magnetisnie quand la force de I'aimant dimi- 
nue, ou quand la distance des poles augmente " * : but many 
of the curious phaenomena from which M. Pliicker was led 
to this conclusion, and which he adduces in confirniation of 
it, do not appear to me to support it, but rather to be con- 
nected with the peculiar magneto-inductive properties of cry- 
stalline or quasL-crystalline structure which he discovered 
subsequently f '•> and with respect to those which appear at 
first sight really to support it, I have conjectured that they 
may admit of explanation solely on the principle expressed in 
Faraday's law, quoted at the commencement of these remarks. 
Thus, the experiments upon a watch-glass containing mer- 
cury, placed at different distances from a magnet, which show 
that the resultant force experienced by the watch-glass, in 
virtue of its own magnetization as a ferromagnetic substance, 
and the contrary magnetization of the diamagnetic mercury, 
is sometimes increased by removing the whole to a slightly 
greater distance from the magnet, do not prove that when the 
magnetizing force is diminished the induced magnetization of 
the mercury is diminished by a greater fraction of its former 
amount than that of the watch-glass, but are most probably 
to be explained by the circumstance that the " field of force" 
occupied by the mercury and watch-glass, when removed a 
very short distance, is such that the mean value of the differ- 
ential coefficient of the square of the force, with reference to 
co-ordinates parallel to the direction of motion of the watch- 
glass, is greater than the mean value of the same function, 
through the field occupied when the watch-glass is in contact 
with the magnet. It is of course impossible to give more than 
a general explanation such as this without some specific know- 
ledge of the distribution of magnetic force in the neighbour- 
hood of the actual magnet employed ; but the phaenomena 
described by M. Pliicker in this case are undoubtedly of a 
kind that might be anticipated if a vertical bar-magnet be 

* Quoted from a paper in the French Annates de Ctiimie et de Pliysique, 
June 1850, bearing the title, " Sur le Magnttisme et le Diamagnetisme : 
par M. Pliicker." This paper appears to be a i-hume oi the author's ex- 
perimental researches and discoveries regarding magnetic induction, of 
which detailed accounts have been published in various communications to 
PoggendorfPs Annalen in the course of the last two years. 

t This connection is recognized by the discoverer himself, as is shown by 
the statement he makes at the commencement of <5 4 of the paper already 
referred to. Yet he mentions his experiments on cylinders of charcoal as 
the foundation on which he establishes, as a general law, the conclusion 
quoted in the text. 

252 Prof. Thomson on the Forces experienced hy indnctively 

used, especially if the upper pole, over which the watch-glass 
is suspended, be flat. An electro-magnet with, for core, a hol- 
low cylinder of soft iron open at the ends, would even repel a 
small ferromagnetic body capible of moving along the axis, 
in some positions, and attract it a little further o{\\ since there 
would be variations of force in this case precisely similar to 
those explained with reference to points in the line of motion 
of the ball in experiment 2. 

22. The most striking experiments adduced by M. Pliicker 
to support his hypothesis, that " tiiamagnetism increases more 
rapidly than magnetism" when the magnetizing force is in- 
creased, are those in which the force experienced by a small 
inductively magnetized body in a constant position is tested 
for different strengths of the same electro-magnet, produced by 
using a greater or less number of cells in the exciting battery. 
At the recent Meeting of the British Association in Edin- 
burgh, I ventured to suggest that a change in the distribution 
of magnetic force in the neighbourhood of the magnet, accom- 
panying an increase or diminution in the strength of the gal- 
vanic current, might have contributed to produce some of the 
singidar phcenomena "•xihich had been observed; and that there 
is some considerable cha?ige in the distributio7i of force in the 
neighbourhood of an electro-magnet isoith a soft iron core iji a 
state of intense magnetization tvhe/i, for instance, the strength 
of the current is doubled, seems extremely pnobable xsohen ix^e con- 
sider that a ]}iece of soft ii'on in a state of inte?ise magnetiza- 
tion cannot be expected to be as open to fresh magnetization as 
it 'would be if not magnetized in the first instance. On the 
same occasion I remarked, that some experiments made by 
Mr. Joule in connexion with his researches on changes of 
dimensions produced in iron bars by magnetic influence, ap- 
peared to indicate diminislied inductive capacities in states of 
intense inductive magnetization*. At that time I was not 
aware of the recent experimental researches ot Gartenhauser 
and Miiller on the magnetization of soft iron ; but 1 have 
since met with a Number of Poggendorff's Ajinalen ( 1 850, 
No. 3, published last April) containing an account of these 
researchesf, which completely confirms the second part of 
the conjecture I had thrown out. Whether or not, how- 
ever, the change in the distribution of force is of such a kind 
as to account for the phaenomena by which M. Pliicker sup- 
ports the conclusion which has been quoted, it is impossible 
to pronounce without a complete knowledge of the circum- 

* Phil. Mag. 1847, vol. xxx. pp. 76, 225. Also Sturgeon's Annals, Aug. 

t " Ueber die Magnetisirung von Eisenstaben diirch den Galvanischen 
Strom ; von J. Miiller." 

Magnetized Non-crystalline Substances. 253 

stances. An experimentum crucis might be made by means of 
an electro-magnet without a soft iron core. 

23. In one respect M. PlUcker's views receive a remark- 
able confirmation by Joule and by Gartenhauser and Miiller's 
experiments, if it be true that a homogeneous diamagnetic 
substance is inductively magnetizable to an extent precisely 
proportional to the magnetizing force, or deviating less from 
this proportionality than the magnetization of soft iron. For 
if a complex body were made up consisting of a diamag- 
netic substance (either solid or in powder) and an extremely 
small quantity of soft iron in very fine powder or filings, 
spread uniformly through it; a small ball of this body would, 
when acted upon by a feeble magnetizing force, become on the 
whole magnetized like a ferromagnetic, and would be urged 
from places of weaker towards places of stronger force. If now 
the magnetizing force were gradually increased, the "resultant 
magnetic moment" of the complex body would at first in- 
crease, then, after attaining a maximum value, decrease to 
zero, after which it would become " negative," or the ball 
would be on the whole magnetized Hke a diamagnetic, and 
would be urged from places of stronger towards places of 
weaker force. Such, if I mistake not, is the bearing which 
M. Pliicker expects of any complex solid consisting of a 
suitable mixture of ferromagnetic and diamagnetic substances; 
but mere experiments on soft iron, such as those of Joule and 
of Gartenhauser and Miiller, do not render it probable that a 
homogeneous feebly ferromagnetic substance, containing no 
iron, or only a very small quantity and that chemically com- 
bined, should have its capacity for fresh magnetization dimi- 
nished by the slight magnetization which the strongest magnet- 
izing force that could be applied would produce. If however 
M. Pliicker's experiments be ultimately admitted as conclusive 
(which I think they certainly must be if those in which the 
position of the substance is unaltered be found to succeed 
with a pure electro-magnet), it would be established that the 
capacity for magnetic induction of a solution of sulphate of 
iron* (ferromagnetic), in water (diamagnetic), would diminish 
as the magnetizing force is increased, becoming zero with a 
certain force ; and negative, so that the liquid would be on the 
whole diamagnetic, with any greater force. 
Row, Gare Loch, Aug. 21, 1850. 

* I assume that the sulphate of iron is in a state of complete sohition, 
as it would be with a slight excess of acid. If the liquid be at all turbid, 
on account of a precipitate of oxide of iron, the phenomena observed by 
M. Pliicker might be explained as in the case of the complex solid con- 
taining soft iron in powder spread through the mass. 

[ 254 ] 

XXX. Oil the Diffusion of Liquids. 
By Thomas Graham, F.K.S.f F,C.S. 

[Continued from p. 198.] 

5. Separation qf^ Salts of different Bases by Diffusion. 

IT was now evident tliat inequality of diffusion supplies a 
method for the separation, to a certain extent, of some salts 
Jroni each other, analogous in principle to the separation of 
miequaliy volatile substances by the process of distillation. 
The potash salts appearing to be always more diffusive tiian 
the corresponding soda salts, it follows, that if a mixed solu- 
tion of two such salts be placed in the solution phial, the pot- 
ash salt should escape into the water atmosphere in largest 
proportion, and the soda salt be relatively concentrated in the 
phial. This anticipation was fully verified. 

(1.) A solution was prepared of equal parts of the anhy- 
drous carbonates of potash and soda in 5 times the weight of 
the mixture of water. Diffused from a small thousand-grain 
phial of I'l inch aperture, into 6 ounces of water, for nine- 
teen days, at a temperature above 60°, it gave a liquid of den- 
sity I '0350, containing a considerable quantity of the salts. 
Of these mixed salts, converted into chlorides by the addition 
of hydrochloric acid, 9-i39 grs., being treated with bichloride 
of platinum in the usual manner, gave 19'39 grs. of the double 
chloride of platinum and potassium, equivalent to 5'91 grs. of 
chloride of potassium ; and left in solution 3"44' grs. of chlo- 
ride of sodium : loss O'Oi gr. These chlorides represent 5*46 
grs. of carbonate of potash and 3' 12 grs. of carbonate of soda. 
The salts actually diffused out were therefore in the proportion 
of — 

Carbonate of soda 36*37 

Carbonate of potash 63'63 


(2.) In another similar experiment from a six-ounce phial 
into 8^^ ounces of water, the liquid ofthe water-jar, after twenty- 
five days' diffusion, contained the two carbonates in nearly the 
same proportions as before, namely — 

Carbonate of soda 35*2 

Carbonate of potash 64*8 


(3.) A partial separation ofthe salts of sea- water was effected 
in a similar manner. 

The sea-water (from Brighton) was of density 1*0265. One 

Prof. Graham o» the Diffusion of Liquids. '255 

thousand grs. of tlie liquid yieWed 35-50 grs, of dry salts, of 
which 2'] 65 grs. were magnesia. The dry salts contain there- 
fore 6*10 per cent, of that earth. 

Six thousand-grain phials, of 1*1 inch aperture, were pro- 
perly filled with the sea-water and placed in six tumblers, each 
of the last containing 6 ounces of water. Temperature about 
50°. The diffusion was interrupted after eight days. The 
salts of the sea-water were now found to be divided as follows: — 

Diffused into the tumblers . 92*9 grs., or 36*57 per cent. 
Remaining in the phials . . 161*1 grs., or 63*43 percent. 

254-0 100*00 

Rather more than one-third of the salts has therefore been 
transferred from the solution phials to the water-jars by dif- 

Of the diff'used salts in the tumblers, 46*5 grs. were found 
to contain 1*90 gr. magnesia, or 4'09 per cent. Hence we 
have the following result: — 

Magnesia originally in salts of sea-water . 6*01 percent. 
Magnesia in salts diffused from sea-water . 4*09 per cent. 

The magnesia, also, must in consequence be relatively con- 
centrated in the liquid remaining behind in the diffusion cells. 

A probable explanation may be drawn from the last results 
of the remarkable discordance in the analysis of the waters of 
the Dead Sea^ made by different chemists of eminence. I 
refer to the relative proportion of the salts, and not their ab- 
solute quantity, the last necessarily varying with the state of 
dilution of the saline water when taken up. The lake in 
question falls in level 10 or 12 feet every year, by evaporation. 
A sheet of fresh water of that depth is thrown over the lake 
in the wet season, which water may be supposed to flow over 
a fluid nearly ] *2 in density, without greatly disturbing it. 
The salts rise from below into the superior stratum by the 
diffusive process, which will bring up salts of the alkalies with 
more rapidity than salts of the earth, and chlorides, of either 
class, more rapidly than sulphates. The composition of water 
near the surface must therefore vary greatly, as this process 
is more or less advanced. 

(4.) I may be allowed to add another experiment which is 
curious for the protracted immobility of a column of water 
which it exhibits, as well as for the separation occurring, which 
last may be interesting also in a geological point of view. A 
plain glass cylinder with a foot, 1 1 inches in height, and of 
which the capacity was 64 cubic inches, had 8 cubic inches 
poured into it of a saturated solution of carbonate of lime in 

256 Prof. Graham on the Diffusion of Liquids. 

carbonic acid water, containing also 200 grs. of chloride of 
sodium dissolved. Distilled water was then carefully poured 
over the saline solution, so as to fill up the jar, a float being 
used and the liquid disturbed as little as possible in the ope- 
ration. The inouth of the jar was lastly closed by a ground 
glass plate, and it was left undisturbed upon the mantel-piece 
of a room without a fire, from INIarch 20 to September 24< of 
the present year, or for six months and four days. Afterwards, 
on removing the cover, tlie fluid was observed not to have 
evaj)orated sensibly, and it exhibited no visible deposit. This 
I was not surprisetl at, as no deposit a})peared in a similar 
experiment with the jar uncovered, after the lapse of six weeks. 
The liquid in the former jar was now carefully drawn ofl:^ by 
a small siphon with the extremity of both its limbs recurved 
so as to open upwards, in four equal portions, which may be 
numbered from above downwards. Equal quantities of the 
four strata of liquids gave the following proportions of chlo- 
ride of sodium and carbonate of lime: — 


oride of sodium. 

Carbonate of lime. 

No. 1. 



No. 2. 



No. 3. 



No. 4. 



The diffusion of the chloride of sodium has therefore not 
yet reached complete uniformity, although approaching it, 
the proportion of that salt obtained from the top and bottom 
strata being as 11 to 12. But the diffusion of the carbonate 
of lime appears much less advanced, the proportion of that 
substance being as 1 to 4 at the top and bottom of the liquid 
column. The slight difference in density of the strata, it may 
be further remarked, must have been sufficient to preserve 
such a column of liquid entirely quiescent, as shown by the 
distribution of the carbonate of lime, during the considerable 
changes of temperature of the season. 

Chemical analysis, which gives with accuracy the propor- 
tions of acids and bases in a solution, furnishes no means of 
deciding how these acids and bases are combined, or what 
salts exist in solution. But it is possible that light may be 
thrown on the constitution of mixed salts, at least when they 
are of unequal diff'usibility, by means of a diffusion experi- 
ment. With reference to sea-water, for instance, it has been 
a question in what form the magnesia exists, as chloride or as 
sulphate; or how much exists in the one form and how much 
in the other. Knowing however the different rates of diffu- 
sibility of these two salts, which is nearly chloride 2 and sul- 

Prof. Graham on the Dijfusiun of Liquids. 257 

phate 1, and their relation to the diffusibility of chloride of 
sodium, we shoukl be able to judge from the proportion in 
which the magnesia travels in company with chloride of so- 
dium, whether it is travelling in the large proportion of chlo- 
ride of magnesium, in the small pro})ortion of sul[)hate of 
magnesia, or in the intermediate proportion of a certain mix- 
ture of chloride anil sulphate of magnesia. But here we are 
met by a tlifficulty. Do the chloride of magnesium and sul- 
phate of magnesia necessarily pre-exist in sea- water in the 
proportions in which they are found to diffuse? iSIay not the 
more easy diffusion of chlorides determine their forujation in 
the diffusive act, just as evaporation determines the formation 
of a volatile salt — producing carbonate of ammoiiia, for in- 
stance, from hy(irochlorate of ammonia with carbonate of lime 
in the same solution ? We shall see inmiediately that liquid 
diffusion, as well as gaseous evaporation, can jnoduce che- 
mical decou^.positions. 

6. Decomposition of Salts by Diffusion. 

■ (1.) At an early period of the inquiry, a solution was dif- 
fused of bisulphate of potash, saturated at 68' and of density 
1*280, from the six-ounce phial of 1175 inch aperture, into 
20 ounces of water. The period of diffusion extended to fifty 
days. About the middle of that period, a few small crystals 
of sulphate of potash, amounting probably to 3 or 4- hun- 
dredths of a grain, appeared in the diffusion cell and never 
afterwards dissolved awaj'. When terminated, the liquid re- 
maining in the solution cell was found of density ri54' ; that 
in the water-jar r0326. A portion of the latter liquid gave 
by analysis — 

Sulphate of potash . . . 20'37 1 r?- i i . c .,,.u 
^, / , ,. ' ,, ,_ >l5isuipnate ot potasfi. 

bulphate or water . . . ll'i/J ' ' 

Sulphate of water . . . 12*77 


It thus appears that the bisulphate of pota-^h ui;deigoes 
ilecompoaition in diffusing, and that the acid diffuses away to 
about double the extent, in equivalents, of the sulphate of pot- 
ash. This greater escape of the acid will also account for the 
deposition of^ crystals of the neutral sulphate in the solution 

(2.) A similar experiiVient was made with another double 
sulphate of greater stability, common potash alum. The so- 
lution of -i anhydrous alum in 100 water, was diffused from 
the six-ounce phial into 24^ ounces of water, at 64'°*2, lor eight 
days. The quantity of salt diffused in that time amounted 
only to 7*48 grs. It contained 106 gr. alumina, which is 

PhiU Macr. S. 3. Vol. 37. No. 250. Oct. 1850. S 

258 Prof. Graham on the Diffiision of Liquids, 

equivalent to 5'33 grs. ot alum. The diiFused salt gave off" 
no acitl vapours at 600 . We may therefore suppose the ex- 
cess of salt which is diirused to be sulphate of potash. The 
ditlusion product of alum, at QV^^ appears to be — 

Alum 5-33 71-26 

Sulphate of potash . . 2*15 28'74 

~T^ Too^ 

In a second experiment, the diffusion product amounted to 
f3*39 grs., of which 0"95 gr. was alumina ; and it is represented 
by ^'T? alum and 1*52 sulphate of potash. 

In connexion with the low diffusibility of the sulphate of 
alumina of alum, it was found that the addition of caustic 
potash to the alum solution, so as to convert it into an alumi- 
nate of potash, increased the diffusibility of the alumina. The 
diffusion product from the 4 per cent, solution of alum so 
treated contained 1*62 gr. of alumina in one experiment and 
r54' in another. 

As alum is a salt of great stability, it presents a severe test 
of the influence in question. The decomposition of this double 
salt by diffusion was further confirmed therefore in experi- 
ments made by means of the four-ounce diffusion phials of 
1*25 inch aperture, and the alteration which the salt undergoes 
in the process more exactly ascertained. The experiments 
were made at a mean temperature of 57°'9, and lasted seven 
days; the solution employed being of 4 anhych'ous alum to 
100 water, as before. 

In three experiments, the salt diffused out amounted to 
5*73, 5-80 and 5*65 grs.; of which the mean is 5*73 grs. The 
latter quantity gave 0*82 alumina and 3*22 sulphuric acid, 
which correspond to 4'11 anhydrous alum and 1*62 neutral 
sulphate of potash. Or, we have as the diffusion product of 
alum, in 100 parts — 

Alum 71-73 

Sulphate of potash .... 28-27 

This analysis corresponds closely with the diffusion product 
of the former experiments, which gave 71-26 per cent, of alum. 
The solution of alum which remains behind in the solution 
phials must of course acquire an excess of sulphate of alumina. 
The salt, sulphate of alumina, did not appear to be decom- 
posed when diffused alone. A four per cent, solution of the 
hydrated sulphate of alumina, which is manufactured at New- 
castle, when diffused in the same circumstances as the prece- 
ding solutions of alum, gave 3*40 grs, of anhydrous sulphate 
of alumina, in which the acid was to the alumina as 2*95 equi- 
valents of the former to 1 equivalent of the latter, or as nearly 

Prof. Graham on the Diffusion of Liquids. 259 

as possible in the proportion of 3 equivalents of acid to 1 of 
base. As the Newcastle salt contained almost exactly half its 
weight of water, the S'lO grs. of anh3'drous salt difCused out 
are equivalent to 6"80 grs. of hydrated sulphate of alumina. 
The sulphate of alumina appears thus to be more diftusive 
than the double sulphate of alumina and potash, in the pro- 
portion of 6*80 to 5"73. 

(3.) It was interesting to observe what really diflPuses from 
the ammoniated sulphate of copper (CuO, SO^ 2NH^ + HO), 
and to find if the low diffusibility of that salt is attended with 
decomposition. The diffusion of the ammoniated sulphate of 
copper was therefore repeated from a 4 per cent, solution in 
the six-ounce solution phial, for eight days, at 64?°'2 In eva- 
porating the water of the jar afterwards, the ammoniated sul- 
phate of copper present was necessarily decomposed, by the 
escape of ammonia, and a subsulphate of copper precipitated. 
The copper found, however, was estimated as neutral sulphate 
of copper. The diffusion product of two experiments may be 
represented as follows, in grains : — 

Sulphate of copper . . . 0-81 097 

Sulphate of ammonia . . 5'^Q 5*53 

6-27 6-50 

The abundant formation and separation of sulphate of am- 
monia in these experiments, prove that the ammoniated sul- 
phate of copper is largely decomposed in diffusion. 

(4.) Perhaps the most interesting result of this kind is a 
solution which is given of the problem of the decomposition of 
the alkaline sulphates by means of lime. 

Solutions were prepared of ~ per cent, of sulphate of potash 
and of chlorides of potassium and sodium in liuie-water. Two 
solution phials were filled with each of these solutions, and 
placed for diffusion in water-jars filled with lime-water, at 49% 
for seven days. 

In the sulphate no deposition of crystcillized sulphate of 
lime took place within the solution phial, while the water- 
jar acquired an alkaline reaction, which remained after preci- 
pitating the lime entirely by carbonic acid gas and evaporating 
twice to dryness. Hydrate of potash, it will afterwards ap- 
pear, is an eminently diffusive salt, having double the diffusi- 
bility of sulphate of potash. The tendency of the former to 
diffuse enables the affinity of the lime for sulphuric acid to 
prevail, and the alkali is liberated and diffused away into the 
external atmosphere of lime-water. By the latter, hydrate of 
lime is returned to the solution cell and the decomposition 
continued. The salt diffused in the two cells amounted to 
2"60 grs., of which 0'62 gr., or 23"85 per cent., was hydrate 


260 I'rof. Graham on the Diffusion of Liquids. 

of potash. The chlorides of potassium and sodium, on the 
contrary, were not sensibly decomposed. 

It is known that a precipitation of sulphate of lime may 
occur, with a larger proportion of sulphate of |K)tash in lime- 
water, in a close phial without external diffusion. As the 
decom}H)sition of the sulphate of potash, in the latter case, 
lias been referred to the insolubility of the sulphate of lime, 
so the decoinposition in the former circumstances is referred, 
in a similar sense, to the high difFusibility of hydrate of potash. 

7. Diffusion of Double Salts. 

How is the diffusion of two salts affected by their condition 
of combination as a double salt? A solution of the double 
sulj)hate of magnesia and potash, in the proportion of 100 
water to 4 anhydrous salt, was operated upon in the four- 
ounce diffuision })hials of 1'25 inch aperture, with a period of 
diffusion of seven days, at 57°'9 F. The diffusion product 
of the double salt was 8*09 and 7'81 grs. in two experiments: 
mean, 7'95 grs. 

The constituent salts, sulphate of magnesia and sulphate of 
potash, were now dissolved separately, in the proportions in 
whicii they existed in the double salt, namely, 1*65 gr. anhy- 
drous sulphate of magnesia in 100 water, and 2 35 grs. sul- 
phate of potash in 100 water, making up together 4 parts of 
salts. The two solutions thus contain equivalent quantities 
of the different sulphates. 

The separate diffusion of the sulphate of magnesia was 2*09, 
2*11 and 2*40 grs. in three cells; and of the sulj)hate of pot- 
ash, 5*83, 5*97 and 5*.54 grs. in three cells; the circumstances 
of the experiments being the same as those of the double salt. 
The means of the two salts are 2*20 and 5"78 grs.; and the 
sum of the two means 7"98 grs. The result is, that the sepa- 
rate diffusion of the constituent salts is almost identical with 
their diffusion when combined as a double salt: — 

Diffusion of the double sulphate of magnesia and! ^ _ _ 

, , r 7*9o grs. 

potash J ° 

Diffusion of equivalents of sulphate of magnesia} „, 

and sulphate of potash in separate cells . . J ^ * 

It would thus appear that the diffusibility of this double 
salt is the sum of the separate diffusions of its constituent salts. 

It has been a question whether a double salt is formed at 
once when its constituent salts are dissolved together, or not 
till the act of crystallization of the compound salt. Equiva- 
lents of the same two sulphates, making up 4 parts, were dis- 
solved together without heat in 100 water. Now the diffusion 
from this mixture, which has the composition ofihe preceding 

Prof. Graham 07i the Diffusion of Liquids. 261 

solution of tlie double salt, exhibited notwithstanding a sen- 
sibly different result of diff'iision, giving 7'28, 7*37 and 7*26 
grs. in three cells; niean,7"30 grs. The diffusion of the double 
salt was greater, namely, 7 95 grs. Hence a strong presump- 
tion that the mixed salts last diffused were not combined, and 
that the double sulphate of magnesia and potash is not neces- 
sarily formed immediately upon dissolving together its consti- 
tuent salts. 

In early experiments of a similar nature made upon the 
double salt, sulpliale of copper and potash, and upon a mix- 
of the two sulphates newly dissolved together, a similar result 
was obtained. Wiiile the diff'usion of the mixed salts was 
2.5"6 grs., that of the same weight of the combined salts (the 
double sulphate) was 30 grs. The double salt appears more 
diffusible, in both cases, than its mixed constituents. 

These double salts appear to dissolve in water without de- 
composition, although the single salts may meet in solution 
without combining. Hence in a mixture of salts we may have 
more than one state of equilibrium possible. And when a 
salt, like alum, happens to be dissolved in such a way as to 
decompose it, the constituents are not necessarily reunited by 
subsequent mixing. Many practices in the chemical arts, 
which seem empirical, have their foundation possibly in facts 
of this kind. 

8. Diffusion of one Salt into the Solution of another Salt. 

It was curious and peculiarly important, in reference to the 
relation of liquid to gaseous diff'usion, to find whether one salt 
A would diff'use into water already charged with an equal or 
greater quantity of another salt B, as a gas a freely diffuses 
into the space already occupied b}' another gas b; the gas b 
in return diffusing at the same time into the space occupied 
by a. Or whether, on the- contrary, the diff'usion of the salt 
A is resisted by B. The latter result would indicate a neu- 
tralization of the water's attraction, and a kind of equivalency 
or equality of power and exchangeability of different salts, in 
respect of that effect, which would divide entirely the phaeno- 
mena of liquid from those of gaseous diffusion. 

(1.) A solution of 4 parts of carbonate of soda to 100 water, 
of density r0406, was placed in the six-ounce diffusion phial 
of 1*175 inch aperture, and allowed to communicate with 24- 
ounces of water. 

Two similar diffusion phials, equally charged, were im- 
mersed in 24' ounces of a solution of 4 parts of chloride of 
sodium to 100 water, having the density 1'0282. The diff'u- 
sion proceeded for eight days, in all cases, at 61'^. The pro- 
portion of carbonate of soda found without in the water-jar 

262 Prof. Graham on the DiJ/usion of Liquids. 

afterwards, was ascertained by an alkalimetrlcal process, the 
neutralization being edected at the boiling-point. The follow- 
ing are the results: — 

Experiment I. Diffusion product"! 906 grs. of carbonate of 

into water J soda. 

Experiment II. Diffusion product^ 8'82 grs. of carbonate of 

into solution of chlorideof sodium J soda. 
Experiment III. Diffusion product 1 9*10 grs. of carbonate of 

intosolution of chloride of sodium j soda. 

It thus appears that 4 per cent, of chloride of sodium 
present in the water atmosphere of the jar has no sensible 
effect in retarding the diffusion into it, from the solution cell, 
of carbonate of soda from a solution containing also 4 per 
cent, of the latter. 

(2.) The experiment was varied by allowing the solution 
of carbonate of soda to diffuse into a solution of sulphate of 
soda, a salt more similar to the former in solubility and com- 
position. The solution of the latter, containing 4 per cent., 
was of density 1*0352. The temperature and period of dif- 
fusion were the same as before: — 

Experiment IV. Diffusion product! 7'84 grs. of carbonate of 

into solution of sulphate of soda j soda. 
Experiment V. Diffusion product^ 7"82 grs. of carbonate of 

into solution of sulphate of soda J soda. 

Here we find a small reduction in the quantity of carbonate 
of soda diffused, amounting to one-eighth of the whole. The 
sulphate of soda has therefore exercised a positive interference 
in checking the diffusion of the carbonate to that extent. So 
small and disproportionate an effect however is scarcely suffi- 
cient to establish the existence of a mutual elasticity and re- 
sistance between these two salts. 

Still it might be said, may not the diffusion of one salt be 
resisted by another salt which is strictly isomorphous with the 

(3.) A solution of 4 parts of nitrate of potash to 100 of 
water, of density 1*0241, placed in the solution phial, was 
allowed to communicate with water containing 4 per cent, of 
nitrate of ammonia in the water-jar, which last solution was 
of density 1*0136; with all other circumstances as before. 
With one solution phial having the usual aperture, 1*175 inch, 
the diffusion product was 15*32 grs. of nitrate of potash. With 
a second phial, having a larger aperture of ri90 inch, the 
diffusion product was 18*03 grs. of nitrate of potash. No 
comparative experiment, on the diffusion of nitrate of potash 
into water, was made at the same time. But nitrate of am- 
monia, which appeared before to coincide in diffusibility with 

Prof. Graham on the Diffusion of Liquids. 2(33 

nitrate of potash, gave on a former occasion, in similar cir- 
cumstances, and at 61'°'9, nearly the same temperature, a dif- 
fusion product of 15"80 <i,rs. Tlie quantity of nitrate of pot- 
ash (15-32 grs.) which diffused into the sohition of nitrate of 
ammonia approaches so closely to the number quoted, that 
we may safely conclude that the diffusion of nitrate of potash 
is not sensibly resisted by nitrate of ammonia, although these 
two salts are closely isomorphous. They are still therefore 
inelastic to each other, like two different gases. 

These experin^ents have been made upon dilute solutions, 
and it is not at all impossible that the result may be greatly 
modified in concentrated solutions of the same salts, or when 
the solutions approach to saturation. But there is reason to ap- 
prehend that the phaenomena of liquid diffusion are exhibited 
in the simplest form by dilute solutions, and that concentration 
of the dissolved salt, like compression of a gas, is attended 
often with a departure from the normal character. 

On approaching the degree of pressure which occasions the 
liquefaction of a gas, an attraction appears to be brought into 
play, which impairs the elasticity of the gas ; so on approach- 
ing the point of saturation of a salt, an attraction of the salt 
molecules for each other, tending to produce crystallizationj. 
comes into action, which will interfere with and diminish that 
elasticity or dispersive tendency of the dissolved salt which 
occasions its diffusion. 

We are perhaps justified in extending the analogy a step 
further between the characters of a gas near its point of lique- 
faction and the conditions which we may assign to solutions. 
The theoretical density of a liquefiable gas may be completely 
disguised under great pressure. Thus, under a reduction by 
pressure of 20 volumes into 1, while the elasticity of air is 
19' 72 atmospheres, that of carbonic acid is only 16' 70 atmo- 
spheres, and the deviation from their normal densities is in 
the inverse proportion. Of salts in solution the densities may 
be affected by similar causes, so that although different salts 
in solution really admit of certain normal relations in densit}', 
these relations may be concealed and not directly observable. 

The analogy of liquid diffusion to gaseous diffusion and 
vaporization is borne out in every character of the former 
which has been examined. Mixed salts appear to diffuse in- • 
dependently of each other, like mixed gases, and into a water 
atmosphere already charged with another salt as into pure 
water. Salts also are unequally diffusible, like the gases, and 
separations, both mechanical and chemical (decompositions), 
are produced by liquid as well as by gaesous diffusion. But 
it still remains to be found whether thediffusibilities of differ- 
ent salts are in any fixed proportion to each other, as simple 

264 Prof. Graham on the Diffusion of Liquids. 

numerical relations are known to prevail in the difiusion velo- 
cities of the gases, from wiiich their densities are deducible. 

It was desirable to make numerous simultaneous observa- 
tions on the salts compared, in order to secure uniformity of 
coniiitions, particularly of temperature. 'I'he means of greatly 
multiplying the experiments were obtained by having the so- 
lution phial cast in a mould, so that any number of solution 
cells could be procured of the same form and dimensions. 
The phials were of the form represented (fig. 3), Yxq. 3. 
holding about 4 ounces, or more nearly 2080 grs. of fZ~^ 
water to the base of the neck, and the mouths of all J I 
were ground down, so as to give the phial a uniform 
height of 3*8 inches. The mouth or neck was also 
ground to fit a gauge-stopper of wood, which was 
0'.5 inch deep and slightly conical, being \"2.\ inch 
in diameter on the upper, and 1'20 inch on the lower 

surface. These are therefore the dimensions of the 

difiusion aperture of the new solution cells. A little 
contrivance to be used in filling the phials to a constant di- 
stance of half an inch from the surface of the lip, proved useful. 
It was a narrow slip of brass plate, having a descending pin 
of exactly half an inch in length fixed on one side of it (fig. 4). 
This being laid across the 
mouth of the phial with the Fig. 4. 

pin downwards in the neck, 
the solution was poured into 
the phial till it reached the 
point of the pin. The brass 
plate and pin being removed, 
the neck was then filled up 
with distilled water, with the aid of the little float as before 
described. The water-jar, in which the solution phial stood, 
was filled up with water also as formerly, so as to cover the 
phial entirely to the depth of 1 inch. This water atmosphere 
amounted to 8750 grs., or about 20 ounces. A glass plate 
was placed upon the mouth of the water-jar itself to prevent 
evaporation. So.nnetimes 80 or 100 diffusion cells were put 
in action at the same time. The period of diffusion chosen 
was now always exactly seven days, unless otherwise men- 

II. Diffusion of Salts of Potash and Ammonia. 

Solutions were prepared of the various salts, in a pure state, 
in certain fixed proportions, namely, 2, 4, 6| and 10 parts of 
salt to 100 parts of water by weight. The density of these 
solutions was observed by the weighing-bottle, at 60°. The 
solutions were frequently diffused at two different tempera- 

Prof. Graham on the Diffusion of Liquids, 265 

tiires; one, the temperature of the atmosphere, which was 
fortunately remarkably constant durintr most of the experi- 
ments to be recorded at jiresent, and the other, a lower tem- 
perature, obtained in a close box of large dimensions, con- 
taining masses of ice. Tiie results at the artificial temperature 
were obviously less accurate than those of the natural tempe- 
rature, but have still considerable value. Three experiments 
were generally made upon the diffusion of each solution at the 
higher, with two experiments at the lower temperature. 

(1.) The carbonate and sulphate of potash and sulphate of 
ammonia were first diffused during a period of seven days, of 
which the temperatures observed by a thermometer placed 
near the water-jars were 6^°-5, 65^, 63°-5, 63°, 63'', 63°-5, 65° 
and Q6° ; mean temperature 64'°*2. 

Table VII. — Diffusion of Carbonate of Potash, Sulphate of 
Potash and Sulphate of Ammonia. 

Parts of anhydrous salt to 100 water. 

Density of 

solution at 


At 64°-2. 

At 37°-6. 





Carbonate of potash. 






























Sulphate of potash. 






























Sulphate of ammonia, NH'*0, SO'. 




















10 94 










266 Prof. Graliam o)i the DiJ)]ision of Liquids. 

The dilTusion product was obtained by evaporating the 
water of each jar separately as before, and the result is ex- 
pressed in grains. 

It will be observed at once, on comparing the means of the 
experiments, that the three salts under consideration are re- 
markably similar in their diffusion, particularly with the smaller 
proportions of salt. Thus the mean diffusion of the 2, 4, 6f 
and 10 parts of the salts is as follows: — 

Diffusion at 64°-2. 





Carbonate of potash ... 

Sulphate of potash 

Sulphate of ammonia... 







4. 1 6|. 

Carbonate of potash 




Sulphate of potash 

Sulphate of ammonia 

The proportions diffused are sensibly equal, of the different 
saltSj at the higher temperature, with the exception of the 
largest proportion of salt, 10 per cent, when a certain diver- 
gence occurs. This last fact is consistent with our expecta- 
tions, that the diffusion of salts would prove most highly 
normal in dilute solutions. Some of the irregularities at the 
lower temperature are evidently of an accidental kind. 

(2.) The neutral chromate and acetate of potash were dif- 
fused at a temperature ranging from 63° to 6b°,) or at a mean 
temperature of SI-^-l, which almost coincides with the higher 
temperature of the last experiments. 

Prof. Graham on the Diffiision of Liquids. 267 

Table VIII. — Diffusion of Chromate of Potash and Acetate 
of Potash, at 64-''-l. 

Parts of anhydrous salt 
to 100 water. 

Density of 
solution at G0°. 



Chromate of potash. 






















Acetate of potash. 





















We have the same dose correspondence in the diffusion 
products of these two salts as in the ])receding group, and 
here the correspondence extends to the 10 per cent, solution. 

Diffusion at 64°' 1. 





Chromate of potash ... 
Acetate of potash 






The 10 per cent, solution of these two salts also agrees with 
the same solution of carbonate of potash, which was 24-69 grs. 
Nor do the lower proportions diverge greatly from the pre- 
ceding group of salts. 

268 Prof. Graham oti the Di/ftision of I J quids. 

{3.) Another pair of salts were simultaneously diffused, but 
with an accidental difference of O"*^ of temperature. 

Table IX.— Diffusion of Bicarbonate of Potash, KO, CO^ 
+ HO, CO^ at Gt°- 1 , and Bichromate of Potash, KO, 2Cr03, 
at 6\^-5. 

Parts of anhydrous salt to 100 

Density of 
solution at 6u°. 

At6l°-1 and64°-5. 



Bicarbonate of potash. 












Bichromate of potash. 











Here again the two salts approach closely in diffusion, and 
also correspond well with the tvvo preceding series. 

Mean Diffusion at 64-°-l and 64.^-5. 




11 01 

Bichromate of potash 

It is singular to find that salts differing so much in consti- 
tution and atomic weight as the chromate and bichromate of 
potash, may be confounded in diffusibility. The diffusion 
products of these two salts are, for the 2 per cent, solutions, 
5"77 and 5-66 grs., and for the 4 per cent, solution, 11 '19 and 
11*49 grs. The bicarbonate of potash also exhibits a consi- 
derable analogy to the carbonate, but resembles still more 
closely the acetate. It is thus obvious that equality, or simi- 
larity, of diffusion is not confined to the isomorphous groups 
of salts. 

(4.) The nitrates of potash and ammonia have already ap- 
peared to be equidiffusive at two different temperatures. 
They were diffused again in the same proportions as the last 
salts, at a temperature varying from 63^^ to 67"'5. 

Prof. Graham on the Diffusion of Liquids. 269 

Table X. — Diffusion of Nitrate of Potash and Nitrate of 
Ammonia at 65°'9. 

Parts of anhydrous salt to 100 

Density of solu- 
tion at 6o°. 



Nitrate of potash. 







Nitrate of ammonia Nil-' 0, NO*. 





34 22 

The sohition of nitrate of ammonia of the water-jars was 
evaporated carefully at a temperature not exceeding 120° F., 
to prevent loss of the salt by sublimation or decomposition. 

Diffusion at 65°-9. 





Nitrate of potash 





Nitrate of ammonia 

Although these salts correspond closely, it is probable that 
neither the diffusion of these nor the" diffusion of any others is 
absolutely identical. The nitrate of ammonia appears to 
possess a slight superiority in diffusion over the nitrate of pot- 
ash, which increases with the large proportions of salt in solu- 
tion. They are both considerably more diffusible than the 
seven preceding salts. 

(5.) A second pair of isomorphous salts were compared, 
the chlorides of potassium and ammonium. 

270 Prof. Graham on the Diffusion of Liquids. 

Table XI. — Diffusion of Chloride of Potassium and Chloride 

of Ammonium. 

At 66<>-2. 

At 64°-7 

Piirts of anhydrous salt to 100 

Density of so- 
lution at 6o°. 




Mean . 



Chloride of potassium. 

















15 07 
















Chloride of ammonium. 





















24 13 






These two salts agree well in diffusibility, and are also evi- 
dently related to the preceding nitrates. The quantity of 
chloride of ammonium diffused was determined by evapora* 
tion, which is troublesome and may lead to small errors, from 
the volatility and efflorescent tendency of this salt. It would 
be easier and more accurate to determine this and other chlo- 
rides by the use of a normal solution of nitrate of silver, and 
so avoid evaporation. 

Diff"usion at 66°-2. 





Chloride of potassium 
Chloride of aramoniutu 






The quantities diffused of these two chlorides are more 
closely in proportion to the strength of the original solution, 
than with any of the preceding salts of potash. Thus the 
quantities diffused from the 2 and 10 per cent, solutions of 
chloride of potassium are 7"70 and 3()'93 grs., which are as 2 
to 9*6, which is nearly as 2 to 10. Chloride of sodium was 
observed before to be nearly uniform in this respect; but other 
salts appear to lose considerably in diffusibility with the higher 

Prof. Graham 07i the Diffusion of Liquids. 271 

proportions of salt. It is possibly a consequence of the cry- 
stallizing attraction, to which reference was lately made, coming 
into action in strong solutions and resisting diffusion 

(6.) The diffusion of chlorate of potash was observed at a 
temperature ranging from 63° to 65°^ of which the mean was 

Table XII. — Diffusion of Chlorate of Potash. 

Parts of salt to 100 water. 

Density of solu- 
tion at 60°. 

At 64°-l 













6-5 (saturated solution). 





The solutions of chlorate of potash must be evaporated and 
the residuary salt dried at a temperature not exceeding 212°, 
otherwise a very sensible quantity of chloride of potassium 
may be formed. The chlorate appears to be sensibly inferior 
in difflisibihty to the nitrate of potash. From the 4 per cent, 
solution of the chlorate we have a diffusion product of 13*27 
grs., and from the corresponding solution of the nitrate 13"97 
grs. ; but the latter was obtained at a temperature 1°"8 higher 
than the former. It remains a question whether chlorate of 
potash does not really belong to the nitre group of salts, but 
has its diffusion interfered with by some secondary agency, 
such as its sparing solubility and consequent nearer approach 
to the saturating proportion. 

It is certainly true that the uniformity of diffusion generally 
increases with the dilution of the solutions. This appears on 
comparing the diffusion of the 4 per cent, solution of what 
may be called the sulphate of potash group, with the diffusions 
of the 2 per cent, solutions of the same salts. 

Diffusion of Salts of the Sulphate of Potash Class. 

1 4. 


Carbonate of potash 

Sulphate of potash 

Sulphate of ammonia 

... 10-27 
...| 10-57 
... 10-51 


Acetate of potash 

Bicarbonate of potash ... 

Chroraate of potash 

Bichromate of potash ... 

... 10-70 

... 11-01 
... 11-19 
... 11-49 

272 Prof. Graham on llic Diffusion of Liquids. 

Thus while the 4 per cent, solutions range from 10*27 to 
ir4-9 grs., or from 100 to IITS, the 2 per cent, solutions 
range from 5*45 grs to 5*85 grs., or from 100 to 107*3. 

As it appeared to be in dilute solutions that the greatest 
uniformity of diffusion is to be expected, a series of experi- 
ments was instituted upon the preceiling salts, with the ad- 
dition of acetate of potash, which appeared to belong to the 
same class, the solution enipioyed being that of 1 salt to 100 
water. The experiments were made in a vault, of which the 
temperature was nearly uniform, falling in a gradual manner 
from 59° to 58% with a mean of 58°'5 during the period of 
seven days which the diffusion lasted. Eight phials of each 
salt were diirused, and the li(juids of four water-jars evaporated 

Carbonate of potash gave 10"42 and 10 59 grs. of salt dif- 
fused: mean 10*51 grs., or 2*63 grs. for one cell. 

Sulphate of potash gave 10*72 and 10*78 grs. of salt dif- 
fused: mean 10*75 grs., or 2*69 grs. for one cell. 

Acetate of potash, its diffusion product being treated with 
an excess of hydrochloric acid, gave 8*30 and 8*0 1 grs. of 
chloride of potassium, equivalent to 10"91 and 10*57 grs. of 
acetate of potash; mean 10'74' grs. of acetate of potash, or 
2*68 grs. for one cell. The diffusion of these three salts is 
therefore remarkably similar: — 

Diffusion of 1 per cent, solufions at 58°*5. 

Carbonate of potash .... 2*63 grs. 
Sulphate of potash .... 2'69 grs. 
Acetate of potash .... 2*68 grs. 

The 1 jier cent, solution of neutral or yellow chromate of 
potash in good crystals gave 11*28 and 11-35 grs.; mean 
11*31 grs., or 2*83 grs. for each cell. It was remarked of the 
diffused chromate in this experiment, that it contained a sen- 
sible quantity of green oxide of chromium. The diffusion of 
a salt appears indeed to try its tendencies to decomposition 
veiy severely. 

The bicarbonate of potash gave 8'83 and 8*35 grs. of chlo- 
ride of potassium, the diffusion product being neutralized with 
hydrochloric acid; equivalent to 11*25 and 11*21 grs, of bi- 
carbonate of potash ; mean 1 1*23 grs., or 2*8 1 grs. for one cell. 

The bichromate of potash gave 11*54' and ll*i9grs. of salt 
diffused; mean 11*51 grs., or 2*88 grs. for one cell. These 
last three salts give all a larger diffusion product than the 
preceding three, while they agree well together. It is doubtful 
whether this excess in their diffusion is occasioned by a par- 
tial decomposition in the act of diffusion, which might be of 

Prof. Graham on the Diffusion of Liquids. 273 

such a kind as to increase the real or apparent diffusion in 
every one of them, or whether it is a peculiar character of this 
little group, to which the ferricyanide of potassium, it will be 
afterwards seen, falls to be added, while the ferrocyanide ap- 
pears to belong to the other group : — 

Diffusioji of 1 per cent, solutions at 58°"5. 

Chromate of potash .... 2-83 grs. 
Bicarbonate of potash . . . 2'81 grs. 
Bichromate of potash . . . 2*88 grs. 

The divergence from each other of two salts so closely iso- 
morphous as sulphate and chromate of potash, in the propor- 
tion of 100 to 105*2, is certainly remarkable, unless due to a 
slight decomposition of the latter. 

(7.) Ferrocyanide and Ferricyanide of Potassium. 

Of these two salts the 1 percent, solution only was diffused. 
The time of diffusion was seven days, as usual ; the mean tem- 
perature 5'i!°'5. In evaporating the liquid of the water-jars, 
both salts were partially decomposed, so that it became neces- 
sary to estimate the diffusion product by a determination of 
the potash. Eight cells were employed for one salt and six 
for the other, and the liquitls of the water-jars evaporated two 

The diffusion product of ferrocyanide of potassium (anhy- 
drous) was 5°02, 5*22, 5*02 and 5*20 grs.; mean 5"12grs., or 
for one cell 2*56 grs. 

The diffusion productof ferricyanide of potassium was 5*54, 
5'64! and 5'36 grs.; mean 5*51 grs., or for one cell 2*75 grs. 

Three cells of a similar solution of sulphate of potash which 
were diffused for seven days at a mean temperature 1° lower, 
or of 53°'5, gave 2*56, 2*53 and 2*62 grs. ; mean for one cell 
2*57 grs., a number which almost coincides with that of the 
ferrocyanide of potassium (2-56 grs.). The ferricyanide of 
potassium, on the other hand, is sensibly more diffusive, as 
107"6 to 100, and appears to rank with the bicarbonate and 
bichromate of potash. The ferricyanide of potassium, again, 
is a salt which probably undergoes a slight decomposition in 
diffusion like those salts mentioned : — 

Diffusion of 1 per cent, solutions. 

Sulphate of potash .... 2*57 grs. at 53°*5. 
Ferrocyanide of potassium . . 2*56 grs. at 5^°' 5. 
Ferricyanide of potassium . . 2'75 grs. at 54<^*5. 

The salts of the nitre class may also be compared in the 
Phil. Ma". S. 3. Vol. 37. No. 250. Oct. 1850. T 

274' Prof. Graham on the Diffusion of Liquids. 

same manner, and I shall now add a third series of results 
obtained from the dilTiision of 1 per cent, solutions of the same 
salts. The tem})erature of dillusion of this new series was 
G4'°"5. ISix phials of each salt were diffused, and they were 
evaporated afterwards two and two. This double dilFusion 
product, however, is divided by 2 in the table. 

Diffusion of Salts of the Nitre Class. 




Nitrate of potash 





Nitrate of ammonia 

Chloride of potassium 

Chloride of ammonium 

Chlorate of potash 





It is interesting to observe how the chlorate of potash rises 
in the lower proportions and approaches to the normal rate 
of its class. The diffusion products of all the salts are obvi- 
ously more uniform for the two than for the 4 per cent, solu- 
tions, and again more uniform for the 1 than for the 2 per 
cent, solutions. The extremes in the 1 per cent, solutions 
are 3*66 grs. chlorate of potash, and 3*89 grs. chloride of am- 
monium, which are as I to 1'0628. We have here an ap- 
proach to equality in diffusion, which appears to be as close 
as the experimental determinations are of the specific heat of 
different bodies belonn-ing to one class. The numbers for the 
specific heat of equivalents of the metallic elements are known 
to vary as 38 to 42. 

The salts of potash thus appear to fall into two groups of 
very similar if not equal diffusibility. What is the relation 
between these groups ? 

The diffusion of 4 per cent, solutions of carbonate and ni- 
trate of potash was repeated at a temperature rising gradually 
from 63° to Q5° during the seven days of the experiment, with 
a mean of 64°'l. The diffusion products of the carbonate 
were lO'Sl, 10-05 and 10*44 grs. in three cells; mean 10*27 
grs. Of the nitrate, lS-98, 13*86 and 13*60 grs. ; mean 13*81 
grs. We have thus a diffusion in equal times of — 

Carbonate of potash . . 10*27 1 

Nitrate of potash . . . 13*81 1*3447 

These experiments are almost identical with the former re- 
sults, 10*25 carbonate of potash, and 13*97 nitrate of potash. 
But the numbers thus obtained cannot be fairly compared, 
owing to the diminishing progression in which the diffusion of 

Prof. Graham on the Diffusion of Liquids. 275 

a salt takes place. Thus when the diffusion of nitrate of pot- 
ash was interrupted every tvvo days, as in a former experiment 
with chloride of sodium, the progress of the diffusion for eight 
days was found to be as follows in a 4- per cent, solution, with 
a mean temperature of 6G°. 

'Nitrate of Potash. 

Diffused in first two days . . 4-'54< grs. 

Diffused in second two days . 4*13 grs. 

Diffused in third two days . . 4*06 grs. 

Diflfused in fourth two days . 3*18 grs. 


The absence of uniformity in this progression is no doubt 
chiefly due to the want of geometrical regularity in the form 
of the neck and shoulder of the solution phial. A plain cy- 
linder, as the solution cell, might give a more uniform pro- 
gression, but would increase greatly the difficulties of mani- 

The diffusion of carbonate of potash will no doubt follow a 
diminishing progression also ; but there is this difference, that 
the latter salt will not advance so far in its progression, owing 
to its smaller diffusibility, in the seven days of the experiment, 
as the more diffusible nitrate does. The diffusion of the car- 
bonate will thus be given in excess, and as it is the smaller 
diffusion, the difference of the diffusion of the two salts will 
not be fully brought out. 

The only way in which the comparison of the two salts can 
be made with perfect fairness, is to allow the diffusion of the 
slower salt to proceed for a longer time, till in fact the quan- 
tity diffused is the same for this as for the other salt, and the 
same point in the progression has therefore been obtained in 
both ; and to note the time required. The problem takes the 
form of determining the times of equal diffusion of the two 
salts. This procedure is the more necessary from the inap- 
plicability of calculation to the diffusion progression. 

Further, allowing the Times of Equal Diffusion to be 
found, it is not to be expected that they will present a simple 
relation. Recurring to the analogy of gaseous diffusion, the 
times in which equal volumes or equal weights of two gases 
diffuse are as the square roots of the densities of the gases. 
The times, for instance, in which equal quantities of oxygen 
and hydrogen escape out of a vessel into the air, in similar 
circumstances, are as 4 to 1 ; the densities of these two gases 
as 16 to 1. Or, the times of equal diffusion of oxygen and 
protocarburetted hydrogen are as 1*4142 to 1, that is as the 


276 Prof. Graham on the Diffusion of Liquids. 

square root of 2 to the square root of 1 ; the densities of these 
gases bein<^ 16 and 8, whicli are as 2 to 1. The densities are 
the squares of the ecjual-diirusion times. It is not therefore 
the times themselves of equal (hffusion of two sahs, but the 
squares of those times whicii are likely to exhibit a simple 

(1.) While the 1 per cent, solution of nitrate of potash was 
dilfused as usual ior seven days, the corresponding solution 
of carbonate of potash was now allowed to diffuse for 9*90 
days; times which are as 1 to l*tli2, or as I to the square 
root of 2. 

The results were as follows: diff'used of — 

Nitrate of potash at 64<°*1, in seven days, 13'81 grs. 100 
Carbonate of potash at G^'^'S, in 9-9 days, 13-92 grs. lOO'S 

The three experiments on the nitrate of potash, of which 
13*81 grs. is the mean, were 13*98, 13*86 and 13*60 grs., as 
already detailed. The three experiments on the carbonate 
were 14'-00, 13*97 and 13*78 grs. The difference in the means 
of the two salts is only 0*11 gr. The results appear to be as 
near to equality as could be reasonably expected from the 
method of experimenting. Seven and 9*90 may therefore be 
considered as the times of equal diff'usion indicated for nitrate 
and carbonate of potash. The times of equal diffusion, or the 
diff'usibilities of nitrate and carbonate of potash, would appear 
therefore to be in the proportion of the square root of 1 to 
the s(juare root of 2. 

The explanation of such a relation suggested by gaseous 
diff'usion has been anticipated. It is that the two salts have 
different densities in solution, that of nitrate of potash being 
1, and that of carbonate of potash 2. We are thus led to 
ascribe, what may be called Solution Densities, to the salts. 
The two salts in question are related exactly like protocarbu- 
retted hydrogen gas, of density 1, to oxygen gas of density 2. 
The parallel would be completed by supposing that the single 
volume of oxygen to be diff'used was previously mixed with 
100 volumes of air (or any other diluting gas), while the 2 
volumes of protocarburetted hydrogen were also diluted with 
100 volumes of air; the diluting air here representing the 
water in which the salts to be diff'used are dissolved in the 
solution cell. The time in which a certain quantity of proto- 
carburetted hydrogen would come out from a vessel contain- 
ing 1 per cent, of that gas being 1 (the square root of den- 
sity 1), the time in which an equal quantity of oxygen would 
diffuse out from a similar vessel containing 1 per cent, also 
would be 1*414-2 (the square root of density 2). 

Prof. Graham on the Diffusion of Liquids. 277 

(2.) A solution of 4 parts of sulphate of potash in 100 water 
was diffused simultaneously with the last solution of carbonate 
of potash, and therefore in similar circumstances. The diffu- 
sion products of three experiments were 14" 16, 14*21 and 
14'53 grs.; mean 14*40 grs. This is in the proportion of 
104*27 sulphate of potash to 100 nitrate of potash; so that 
the approximation to equality of diffusion with nitrate of pot- 
ash, in the selected times, is not so close for the sulphate as 
for the carbonate of potash. 

(3.) The diffusion was repeated of 2 per cent, solutions of 
the nitrate and carbonate of potash at a lower temperature by 
abcjut 10°. The temperature of the solutions was rather un- 
steady; ranging from 56° to 52"*25 for the first period of 
seven days, from 5G° to 50°*5 for the period of 9'90 days, and 
from 55° to 50°*5 for a second period of seven days ; the ex- 
ternal atmospheric temperature having fallen during the same 
period more than 20 degrees. Six phials ot each solution 
were diffused and evaporated two together ; so that the results 
are all double quantities. 

At a mean temperature of 54°*.''?, the nitrate of potash gave 
in seven days 12*60 and 12*13 grs.; mean 12*36 grs. 

Again, at a mean temperature of 52°'4, the nitrate of potash 
gave in seven days 11*85, 12*40 and 11*95 grs.; mean 
12*06 grs. 

The carbonate of potash gave in 9*90 days, with a mean 
temperature of 53°*4, 12*69, 12*40 and 12*12 grs.; mean 
12*40 grs. 

The general results are — 

Nitrate of potash, in seven days, at 54°*3 . 12*36 grs. 
Carbonate of potash, in 9*9 days, at 53°*4 . 12*40 grs. 
Nitrate of potash, in seven days, at 52°*4 . 12*06 grs. 

As the first nitrate is 0°*9 above the carbonate and the second 
nitrate 1° below it, we may take the mean of the two nitrates 
as corresponding to the temperature of the carbonate. We 
thus finally obtain, diffused at 53°*4, of — 

Nitrate of potash in seven days, 12*22 grs. . 100 
Carbonate of potash in 9*9 days, 12*40 grs. . 101*47 

The difference in the amount of the diffusion of the two salts- 
in these times is only 0*18 gr., or l^ per cent. 

These last experiments may be held therefore as tending to 
the same conclusion as the former series, although the circum- 
stances were more than usually unfavourable to their success. 
To find whether the same relation existed between the salts 
through a considerable range of temperature, an opportunity 

278 Prof. Graliam on the Diffusion of Liquids. 

was taken during cold weather to repeat the experiments at a 
low temperature. 

(t.) Solutions of 1 salt in 100 water were diffused from 
eight solution cells, for each salt. 'J'he times were increased, 
but the same ratio of 1 to 1*414'2 was preserved between them. 
The liquids of the cells were found to retain a temperature 
ranging slowly between 41 ° and 38°- 8 during the whole period 
of the observations. Sulphate of potash was substituted for 
the carbonate, as of these two equi-diff'usive salts the former 
had been found to be least in accordance with nitrate of pot- 
ash, in the 4 per cent, solutions, and appeared therefore to 
afford the severest test of the relation. 

For nitrate of potash, at a mean temperature of 39°*7, du- 
ring nine days, the diffusion product of two cells together was 
6-97, 6-9S, 6-77 and 6'64- grs. ; mean 6-83 grs. for two cells. 

For sulphate of potash, at the same mean temperature of 
39°*7, during 12*728 days (twelve days, seventeen hours, 
twenty-eight minutes), the diffusion product of two cells 
together was 7*05, 6*93, 7 '28 and 6*90 grs. ; mean 7*04' grs. 
for two cells. 

The general results are — 

Nitrate of potash in nine days at 39°*7 . 6*83 grs. 100 
Sulphate of potash in 12-728 daysat39°'7 7-04 grs. 103*07 

(5.) Solutions of 2 salt in 100 water were diffused simulta- 
neously with the preceding experiments, and in precisely the 
same conditions of time and temperature. 

The diff'usion product of nitrate of potash during nine days, 
at a mean temperature of 39°-7, was 7*03, 6'63, 6-83and6'83 
grs. for one cell ; mean 683 grs. for one cell, or the same num- 
ber as for two cells with the 1 per cent, solution. 

The diff'usion product of sulphate of potash during 12*728 
days was 6*84, and 6*80 ; mean 6*82 grs. for one cell. These 
experiments almost coincide with the number for nitrate of 

Nitrate of potash, 6*83 grs. . . . 100 
Sulphate of potash, 6*82 grs. . . 99*85 

(6.) The existence of the relation in question was also se- 
verely tested in another manner. Preserving the ratio in the 
times of diffusion for the two salts, the actual times were varied 
in duration, in three series of experiments, as 1, 2 and 3. 
The experiments were made in the vault, with a uniformity 
of temperature favourable to accuracy of observation. Eight 
cells of the 1 per cent, solution of each salt were always dif- 
fused at the same time. 

(a.) Nitrate of potash diff'used for 3*5 days, at 47°*2, gave 

Prof. Graham on the Diffiision of Liquids. 279 

for two cells, 3'55, 3-63, 3*33 and 3'51 grs. ; mean for two 
cells, 3*50 grs. 

Sulphate of potash diffused for 4*95 days, at 47'''3, gave for 
two cells, 3'54, 3*31, 3*51 and 3*63 grs.; mean for two cells, 
3\50 grs., or exactly the same as for nitrate of potash above. 

[b.) Nitrate of potash diffused for seven days, at ^S^'G, gave 
6-1, 6*2, 5*9 and 5*92 grs. ; mean for two cells, 6*04 grs. 

Sulphate of potash diffused for 9-9 days, at 4-9°* 1, gave 
6*13, 5*92, 6*18 and 6*59 grs.; mean 6*20 grs., or, excluding 
the last experiment, 6'08 grs. 

Chromate of potash diffused also for 9*9 days, at 49°'l, gave 
6*19, 6*18, 6*40 and 6*38 grs.; mean for two cells, 6*29 grs. 
The difflised chromate presented no appearance of decompo- 
sition on this occasion. 

(c.) Nitrate of potash diff"used for 10*5 days, at 48°, gave 
8*36, 8*95, 8*82 and 8*84 grs. ; mean for two cells, 8*74 grs. 

Sulphate of potash diffused for 14*85 days, at 48°*6, gave 
8*99, 8*94, 8*66 and 8*56 grs.; mean for two cells, 8*79 grs. 

The mean results for the three different sets of periods of 
diffusion are as follows : — 

3*5 and 4*95 /Nitrate of potash, at 47''*2, 3*50 grs. 100 

days \Sulphateofpotash,at47°-3, 3-50 grs. 100 

TNitrate of potash, at 48°*6, 6*04 grs. 100 

7 and 9*9 days<^ Sulphate ofpotash, at 49°*1, 6*20 grs. 102*65 

LChromateofpotash,at49°*l, 6*29 grs. 104*14 

10*5 and 14*85 /Nitrate of potash, at 48°, 8*74 grs. 100 

days /Sulphate ofpotash,at48°*6, 8*79 grs. 100*57 

The concurring evidence of these three series of experi- 
ments appears to be quite decisive in favour of the assumed 
relation of 1 to 1'4142, between the times of equal diffiision 
for the nitrate and sulphate of potash, and consequently of the 
times for the two classes' of potash salts, of which the salts 
named are types. The same experiments are also valuable as 
proving the similarity of the progression of diffiision, in two 
salts of unequal diffusibility. I shall return again to the rela- 
tion between nitrates and sulphates, under the salts of soda. 

(8.) Hydrate of Potash. 

(1.) Eight cells of the 1 per cent, solution of pure fused 
hydrate of potash were diffused for seven days in the vault, 
with a temperature ranging only from 59° to 58°, of which 
the mean was 58°*6. The product of four cells evaporated 
together was 17*57 grs. of hydrate of potash, and of the other 
four cells 17*19 grs. ; mean 17*38 grs., or 4*345 grs. for one 
cell. The hydrate of potash was estimated from the chloride 

280 Pjof. Graham o)i the Diffusion of Liquids. 

of potassium which it gave when saturated with hydrochloric 
acid. The difiiision product of sulphate of potash for seven 
days, at 58^*5, or almost the same temperature, was 10*75 grs. 
for the four cells, as already stated, and conse(|uently 2*64 grs. 
for one cell. It thus appears that the hydrate of potash is 
greatly more dilTusive than the sulphate of potash in the same 
period of seven days, namely, as 4"34-5 to 2"64'. Such a re- 
sult indeed is not inconsistent with the times of equal diffusion 
of these two substances, differing as much as I to 2. 

(2.) Of pure fused hydrate of potash, a 1 per cent, solution 
was diff'used from four cells for 4*95 days at a mean tempera- 
ture of 53°'7, against a 1 per cent, solution of nitrate of potash 
in six cells, for seven days, at a mean temperature 0°'l lower, 
or of 53°*6. The hydrate of potash which difi'used, is calcu- 
lated as before from the chloride of potassium which it gave, 
when neutralized by hydrochloric acid. Hydrate of potash 
diffused from two cells 5'97 and 6*28 grs. ; mean 6*12 grs., 
or 3*06 grs. for a single cell. 

Nitrate of potash diffused from two cells 6*22, 6'54 and 
5'93 grs.; mean 6*23 grs., or 3*11 grs. for a single cell. The 
diffiision of nitrate of potash being lOO, that of the hydrate of 
potash is 98" 2, numbers which are sufficiently in accordance. 
But the times were as I to 1*4142, and their squares as I to 2. 
So far then as this series of experiments on hydrate of potash 
entitles us to conclude, we appear to have for the salts of pot- 
ash a close approximation to the following simple series of 
squares of equal diff"usion times: — 

Squares of Times of Equal Diffiision, or Solution Densities. 

Hydrate of potash ... 1 

Nitrate of potash .... 2 

Sulphate of potash ... 4 

(3.) The hydrate of potash was also diffused at the lower 

temperature, 39°*7, in company with the nitrate and sulphate 

of potash for a period of 6*364 days (six days, eight hours, 

forty-four minutes). 

The I per cent, solution of hydrate of potash gave in eight 
cells, evaporated two together, 6*93, 6*93, 6*93 and 6*89 grs.; 
mean 6*92 grs. 

The 2 per cent, solution of hydrate of potash gave in three 
single cells, 6*77, 6*49 and 7*10 grs.; mean 6*79 grs. 

The diffusion of nitrate of potash in nine days at the same 
temperature, as already detailed, was sensibly the same, or 
6*83 grs. for both the 1 and 2 percent, solutions. The times 
for the two salts were as I to 1*4142. 

The diffusion of hydrate of potash, at 39°*7, may therefore 

Mr. J. Cockle on Impossible Equations. 28 1 

be stated with reference to that of nitrate of potash, for the 
selected times, as follows: — 

Nitrate of potash, 1 and 2 per cent, solutions . 100 
Hydrate of potash, 1 per cent, solution . . . 101*3 
Hydrate of potash, 2 per cent, solution . . . 99*4 

These experiments at the low temperature concur, there- 
fore, with those made at the higher temperature, in proving 
that the times of equal diffusion of the two substances have 
been properly chosen. 

[To be continued.] 

XXXI. On Impossible Equations^ on Impossible Qjiantities, and 
on Tessarines. By James Cockle, Esq.^ M.A.^ of Trinity 
College^ Cambridge; Bar7-ister-at-La'w,ofthe MiddleTemple^, 
[Continued from voi.xxxvi. p, 292.] 

DEFINITIONS. By an impossible equation is meant an 
equation which has no root whatever capable of being 
expressed in terms of the symbols of the ordinary Double 
Algebra. By an impossible quantity is meant the new species 
of imaginary by which an impossible equation is supposed to 
be satisfied. 

* Commimicated by T. S. Davies, Esq., F.R.S. Lend, and Ed., who 
adds the following note. 

" From my having become accidentally involved in the discussion of 
' congeneric surd equations ' (though merely from having called the atten- 
tion of Mr. Horner to Garnier's equation, and not from any contribution 
of my own towards its elucidation), several of my friends, and some gen- 
tlemen who were strangers, have addressed their views on the subject pri- 
vately to me. ThoFe of Mr. Cockle, from the somewhat close agreement 
with my own, and from the form suitable for publication in which they 
were drawn up, 1 have sent for insertion in the Philosophical Magazine. 
Most others were put in forms that would have required modification for 
the purpose ; and this I did not feel myself at liberty to make, lest I should 
fail to express in my own language the exact view of the writers. There 
is one friend, however, a very eminent analyst, who takes a view directly 
opposed to these; and he has given meat different times his own explana- 
tion of most of the equations that have been hitherto mooted. When I 
state that, being opposed to his views (the opposition being founded, as I 
conceive, on the general principles of analysis), and yet having been uni- 
formly unsuccessful in detecting any specific fallacy in his reasoning, I can- 
not view the question as being settled. On this account it is that I think 
the discussion should be kept open ; and I trust that the gentleman to " 
whom I refer will afford us the benefit of having his ' vein of thought' laid 
open in his own way. Exception;; and failing cases are always the most 
instructive subjects of inquiry in every science : — in analysis they always 
betoken something yet left to be seen or done. 

" On one point, however, I wish to be distinctly understood; viz. as not 
expressing the slightest opinion, at present, on the subject of Quaternions, 
Tessarines, or any of the inquiries into which i,j k enter." 

282 Mr. J. Cockle on Impossible Equations. 

As by linear eciuations, taken in their utmost generality, 
we are leti to contemplate ne^atix'C quantity; and as by qua- 
dratics, cubics, and the higher equations, we are in like manner 
led to form the notion of unreal quantity; so by surd or irra- 
tional equations we may be conducted to the idea of iinjios- 
sible quantity. 


1 + \/.r— 4— Vx^\ = W, 

1 — \/a^— 4- + \/x—l = X, 

l_l_ \/a7— 4+ ^.r— 1=Y, 

1— v/.r — 4— ^^— 1=Z. 

Then, by actual multiplication, we obtain 

6 - 2a? + 2 ^/ j:2 - 5a;' + 4 = W. X, 
6-2a'-2 \^x^-5x + '4^ = Y.Z; 
and hence, on multiplication and reduction, 

4(5-a7) = W.X.Y.Z. 

Let WXYZ = V, then 5 is the only value of x which satis- 
fies V = 0. Hence, no value of x other than 5 can make 
either of the factors W, X, Y, or Z equal to zero; for, if so, 
such other value must make one at least of the remaining 
factors infinite, and we should have to subject x to incompa- 
tible conditions. 

Now W = may, by a transposition, be rendered identical 
with the equation (1) given by Garnier at p. 335 of the second 
edition of his ylnahjse, and is satisfied by the value x = 5. But 
X — (which may, by transposition, be rendered identical 
with the equation numbered (2) by Garnier at the page just 
cited) is not satisfied by that value; at least, not if we con- 
sider the symbol v^ to be such that the quantities included 
under it are necessarily affected with (+1)^. This appears to 
me to be the true meaning of that symbol of radicality, provided 
that, in the development of algebra from arithmetic, we adhere 
as closely as we can to the analogies afforded by the latter 
science, in the most general form of which (universal arith- 
metic or arithmetical algebra) all the quantities [i. e. symbo- 
lized numbers) employed are, implicitly at least, considered as 
affected with ( + 1)^. Accordingly I adhered to this view in 
forming the equation which led me to my Theory of Tessa- 
rines, and by which I sought to connect that theory with 
ordinary algebra. There is no real loss of generality by thus 
restricting the symbol \/ . The root corresponding to the 

Mr. R. Phillips on the Magnetism of Steam. 283 

affection ( — 1)- may always be obtained by prefixing the sign 
— to that of radicality. 

Waiving this discussion however for the present, let us 
admit that, in tiie equation X = 0, x may have given to it the 
value x=-5{ — \)~. Then X = is obviously satisfied. But 
the ordinary double algebra is not relieved from its difficulty. 
For neither 5( + l)- nor 5( — 1)- will satisfy either Y = or 
Z = 0. If, in the above instances, the difficulty is to be evaded, 
it is only by greatly refining our solution, and, as it has oc- 
curred to me, by using expressions of the form w ( + 1 )- + wf — 1 )2, 
and by following certain rules respecting our reductions, and 
the signs to be affixed to the radicals, To those who would 
attempt such a complex and artificial system of solution rather 
than admit the existence of an impossible equation I may 
hereafter address some observations. They will however 
probably find, as I have done, that their attempts are unsatis- 
factory, and the results not philosophically admissible. But 
I shall here content myself with remarking, that, by any 
system of rules, however artificial, the difficulty is only thrown 
further back. Thus, the equation 

Vx-\- ^^'+1=0 

is utterly intractable. 

Should the restricted view which I have taken of the sym- 
bol \/ be deemed ultimately inadmissible, it would not be 
difficult to frame a new impossible equation, other than that 
which I have employed in my Theory of Tessarines, and 
which should give us a new imaginary, determined, like the 
unreal quantities of double algebra, by means of an equation, 
and so constituting a natural extension of that algebra. In 
reframing the fundamental equation of the Tessarine Theory, 
or in adopting one which should give rise to a different theory, 
geometric interpretation sliould always be borne in mind, and 
the uniaxal geometry thence arising would be as direct an 
application of algebra as that which occurs in interpreting and 
applying the ordinary double algebra. 

2 Pump Court, Temple, 
August 30, 1850. 

XXXII. 0/i the Mag7ietism of Steam. 
By Reuben Phillips, Esq. 
[Continued from vol. xxxvi. p. oil.] 

, ^T^HE galvanoscope used in the following experiments 

' A is a modification of that formerly described (2.). 

Instead of two astatic needles, I have employed one sus- 

284 Mr. R. Phillips on the Magtietisrn of Steam, 

pended needle, with its directive force partly neutralized by 
placinj^ near it another fixed magnet. In some experiments 
this was done by attaching a magnetized needle to a piece of 
copper wire sliding through a cork stuck on the inside of the 
beaker; this fixed needle lay horizonally under the suspended 
needle, and the degree to which it was necessary to balance 
the earth's magnetism was elfected by means of the copper 
wire. As this adjustment, although in other respects excellent, 
could not be executed with suflicient rapidity, the needle was 
subsequently removed from the copper wire, and the swinging 
needle was partly balanced by a steel magnet placed at a di- 
stance. When the fixeil magnet was applied, it brought the 
marked end of the suspended needle to point about 20 or 30 
degrees west of the position which it otherwise took up; the 
needle of the galvanoscope stood rectangularly to the axis of 
the coils and on the east side. The swinging needle was 1'8 
inch long, and its point, which was observed in the micro- 
scope as before (3, 4.), pointed to the south. A and C stand 
for the same sides of the field of view, and the general mode 
of using the instrument and the zinc screen was as formerly. 
It may be as well to mention that the microscope inverted. 
The steam was usually employed at pressures ranging from 
15 to 25 lbs. on the inch, the magnetism, so far as my expe- 
riments with coils have yet gone, being sensibly the same 
between these limits. A principal reason for using these 
lower pressures was, that the temporary joints and pewter 
coils of the discharging apparatus were much more easily 
kept in order than at the higher pressures. The stop-cocks, 
T-pieces, &c., were such as are generally used about oxy- 
hydrogen blowpipes, and care was taken that they should have 
sufficient steam-way. The temporary joints were made as 
follows: having adequately supported and brought together 
the two ends which it was desired to unite, a strip of co7nmo7i 
sheet caoutchouc about ^ inch wide was wound once round 
the tubes at the juncture, and then a strip of oiled silk about 
an inch wide was wound twice round outside the caoutchouc 
and slightly bound on with fine thread. Three or four rounds 
of a piece of tinfoil rather wider than the silk were now laid 
on and carefully rubbed down smooth, and then well bound 
on with strong thread. 

1 3 1 . A pewter tube 5 feet 7 inches long, having -^^ inch for its 
internal, and /^ inch for its external diameter, was inserted in 
another pewter tube rather shorter, having an internal diameter 
about /y inch and an external diameter of ^^ inch ; the whole 
was then made into a dense cylindrical coil, 3*3 inches long, 
having a cylindrical space 1*2 inch diameter to receive an iron 

Mr. R. Phillips on the Magnetism of Steam. 285 

core. The smaller pewter tube projected from the larger to the 
extent of about 2 inches at one end and *3 inch at the other ; I 
shall call these the longer and shorter ends of the pipes. A 
T-piece was now placed on the longer end of the pipeSjSo that while 
it could receive the discharge from the larger pipe, the smaller 
pipe was allowed to stand through the straight way of the 
T-piece ; a stop-cock was placed on the branch of the T-piece, 
which therefore served to regulate the flow of steam through 
the outer coil. The end of the smaller pipe after its exit from 
the T-piece was^lso furnished with a cock, having a steam- 
way jf^y inch diameter ; I call this stop-cock S. The shorter 
end of the pipes terminated in a short brass connecting piece, 
the steam-way of which was much larger than the combined 
steam-ways of the coil, and this connecting piece served to 
unite the coils with the condenser of the hydro-electric machine. 
The condenser was interposed between the boiler and the 
coils during ail these experiments, but it was always dry, ex- 
cept where it is said that water was placed in it. The coil 
having been thus connected with the boiler, one end of a 
piece of soft iron, 1 inch diameter and 8 inches long, was in- 
serted in the coil ; the iron was supported quite independently 
of the coil, and the axis of the iron and coil of course lay in 
a horizontal plane. Supposing the back of a watch to have 
been placed against the east end of the iron core, the steam 
circulated in a contrary direction to the motion of the hands 
of the watch. 

1 32. The stop-cock on the branch of the T-piece was closed 
and S opened, then, the coil being cool, on opening the cock 
of the boiler, the needle flew across the field of view towards 
C; with a single puff the motion was perhaps through an 
angle of 5°. 

133. The stop-cock on the branch of the T-piece was 
opened a litde, and the cock of the boiler was opened ; an 
agitation of the needle, or a swing to C, was always observed; 
as soon as it subsided and steam issued from the branch stop- 
cock, S was opened, the needle immediately started off' to A; 
the swing, although less than the foregoing, could easily be 
made by successive puffs quite visible to the unassisted eve. 

IS*. The iron was now removed from the coil, and the last 
experiment repeated. On opening S the needle went towards " 
A, and by successive puff's it could be vibrated across the field 
of view and checked by inverse puff's, but the amount of 
motion was much less than when the iron was in the coil; 
thus showing that the iron had been magnetized by this ap- 
parently new magnetic force. The swing to C was also much 
reduced (26.). Water was now placed in the condenser, and I 
think the swing to A became more powerful in consequence. 

286 Mr. R. Phillips om the Magnetism of Steam. 

135. The brass connecting piece which united the short 
end of the pipes to the condenser was taken away from the coil, 
and another T-picce was now placed on the other end of S, and 
the stop-cock removed from the branch of the former T-piece; 
the branches of these T-pieces stood parallel and were united 
by a piece of pewter tube bent like the letter U. The last- 
added T-piece was united to the boiler. By this arrangement 
it will be seen, that on opening the cock of the boiler the steam 
could always enter the outer coil, but not the inner coil unless 
S was open. The iron core was placed in the coil, and the 
steam circulated in the same direction as before. When the 
steam was turned on the swing was to A, whether S was open 
or not, but stronger when S was open. I thought too much 
steam escaped from between the two pipes at their shorter 
end, notwithstanding the end of the outer pipe had been con- 
siderably contracted; this discharge was sufficiently diminished 
by twisting a quantity of thread about the place where the 
larger pipe ended. 

136. The coil being cool and S closed, the cock of the 
boiler was opened ; the needle was much agitated, being driven 
a little in one direction and then in the other very in-egularly, 
but in the main towards A. As soon as the needle became 
tolerably steady I began to open and shut S at the alternate 
vibrations of the needle, but could not obtain a certain swing 
in either direction. The stop-cock S was now closed, and 
afterwards the cock of the boiler, then S was immediately 
opened, which sent the needle rather strongly towards C. 

137. Another stop-cock, V, was now placed at the shorter 
end of the pipes, and affixed so as to receive the steam only 
from the inside coil ; the steam coulil escape from between the 
two coils as in the last experiment (136.). The cocks S and 
V were thrown open ; there was a strong swing to A as before, 
when the cock of the boiler was opened. S was now shut, 
and after sufficient time had elapsed to allow the coil to be- 
come well heated, on working Swith each alternate vibration, 
a scarcely perceptible swing to A was produced when S was 
opened, which swing-producing power generally went off after 
some puffs. V was now closed and the cock of the boiler and 
S opened. On opening V the needle started for C. Both 
the swings to A and C were as strong as before (132, 133.), 
but regarding the direction of the steam, it is to be observed 
they were inverted. 

138. The stop-cock V was now so united to the shorter 
end of the pipes, as to receive the discharge from between the 
coils as well as that of the inside coil. The steam circulated 
in the same direction as the hands of the watch, and the iron 
core was still in the coil. When the cock of the boiler w^as 

Mr. R. Phillips on the Magnetism of Steam. 287 

opened, S and V being previously opened, the needle swung 
to C ; and to A when the cock otthe boiler and S were opened, 
and V then opened. When the iron was removed, the swings 
both to C and A were much diminished. 

139. The coil was removed from the condenser and turned 
about in a direction parallel to the needle, so that the steam 
could enter through V^ and escape through the combination 
of T~pieces at the other end of the pipes ; the steam being, 
in fact, blown through the coils in a direction opposite to that 
of the last experioient. Opening V and S, and then opening 
the cock of the boiler, gave a swing to C. Opening V and 
the cock of the boiler, and then letting out the steam by open- 
ing S, gave the swing to A. The iron core was not used with 
this arrangement. 

140. The coil was moved through an angle of 180° as be- 
fore (19.). Both swings were now reversed, as compared with 
the former experiment; that is, using the steam as before, the 
swing to C became a swing to A, and the swing to A became 
a swing to C. 

l^l. The pewter coil (29.) was united to the condenser by 
a piece of brass, the steam-way of which was of larger dia- 
meter than the bore of the coil. The steam circulated in a 
contrary direction to the hands of the watch. When the cock 
of the boiler was opened, the swing was to A and rather 

14-2. The other end of the pipe of the coil was united by 
the same piece of brass to the condenser, and the steam cir- 
culated in the same direction as the hands of the watch ; the 
swing was still to A. 

143. A stop-cock was now placed on one end of the tube 
of this pewter coil, and the other end was affixed to the con- 
denser, as in the two preceding experiments ; the steam cir- 
culated in a direction contrary to the hands of the watch ; also 
the iron core was placed in the coil. The stop-cock being 
open and the coil cool, turning on the steam produced a 
strong swing to C. The stop-cock was now closed with the 
cock of the boiler open ; on opening the stop-cock at the 
proper positions of the needle, a swing to A was obtained on 
opening the stop-cock, but it was not nearly so strong as the 
corresponding swing with the double coil. The diameter of • 
the steam-way of the stop-cock was ^'y inch. 

144. The iron was now removed. The swing to C when 
the coil was cool, although less, was still very good, as one 
puff sent the edge of the needle rather more than the whole 
length of the micrometrical scale. The swing to A was, how- 
ever, very feeble ; and it required about ten puffs to produce 
a swing one-third the length of the scale. 

288 Mr. R. Phillips on the Magnetism of Steam. 

145. A glass tube 28 inches long was formed into a coil of 
five convolulions. Tiiis glass tube happened to be rather 
conical ; its internal iliameter at one end being -/^f inch, and 
at the other end about /^ inch, and the tube was tj^*^ inch ex- 
ternal diameter. The end of the tube having the larger dia- 
meter was united to the condenser, and the iron was placed 
in the coil ; the steam circulated in a direction contrary to 
that of the hands of the watch. In these experiments, 10 lbs. 
on the inch was found to be an advantageous pressure for the 
steam. On opening the cock of the boiler the needle moved 
towards C; the steam being then shut off", the needle made a 
sudden start towards A ; and I think the force which sent the 
needle towards A was greater than that which moved it to C. 
Three puff's of steam sent the needle nearly across the field 
of view. 

146. The iron was now removed, the swing remained much 
as before ; if there was any difference, I think it was rather 
greater without the iron. After many experiments I thought 
I could perceive that the needle, when the iron was in, did 
not so promptly obey the steam as when the iron was out, but 
seemed to move rather sluggishly, as if the iron resisted the 
production of the magnetic force of the coil. 

147. The end of the tube having the smaller diameter was 
now united to the condenser by the same piece of brass which 
was used in the preceding experiment, and the steam circulated 
in the same direction. The swing, when the steam was turned 
on, was to C, but much more feeble than before, and the coil 
worked better at a higher pressure. I could not perceive that 
the iron varied the magnetic energy of the coil. 

148. It immediately follows from the foregoing experiments 
(132, 135, &c.), that the direction of the magnetism imparted 
to a coil is not directly, if indeed it is at all, connected with 
the direction of the motion of the steam. In these experi- 
ments two magnetic forces are observable, always opposite in 
direction and about equal in power : one of these 1 have be- 
fore shown to be intimately connected with condensation, the 
other is produced under circumstances where condensation 
cannot take place, but where evaporation does. The experi- 
ments (136, 137.) show very conclusively that the friction of 
steam along a pipe, apart from condensation or evaporation, 
produces no magnetic effect. A more complete consideration 
of all these experiments must be deferred until I have finished 
a further set. 

7 Prospect Place, Ball's Pond Road, 
July 27, 1850. 

[ 289 ] 

XX XI II. On a Geometrical Theorem. 
J5j/WiLLiAM Spottiswoode, M.A., ofBalUolCollege^Oxford^, 

IF three cones of the second order, having a common ver- 
tex, cut one another two and two in at least three straight 
lines, and if in each cone there be inscribed a hexahedral 
angle, such that each of the nine straight lines of intersection 
shall be a common edge of two hexahedral angles; then, adopt- 
ing a former notation, the equations to the three cones may 
be written tiius: — 

S(V.VXiA.2-V,a2v,.V.\Vi^,.Vv,Xi.V.VviV,.VX2ju,) = 
S(V.Va,\ . V^v.2 . VAVgJ'^ . VvA, . V.Vv.v . V A^,) = 
S(V.VaX,. V,a,v . V.Vp^jai . VvjA . V.VvViV . A,a) = 




SAAjjm.j ..SjU./ijy . SvvjAj . SA|W,Vj =SAAjV, . Sjw.jw.jA . SvV|jut 
and if these be written thus, 

u=w, u,=w„ u.^w^, . 



the equation 


will be of the fourth order in each of the vectors A, A,, A^, • . > 
and will be satisfied when any of them {c. g. v) is made to co- 
incide successively with each of the others ; (4?.) is consequently 
the equation of a cone of the fourth order, on which all the 
nine edges he. Hence the following 

Theorem. If three cones of the second order, having a com- 
vion vertex, intersect one another txsco and ttico, the nine lines of 
intersection [three being selected from each j^air of cones) 'will 
lie on a cone of the fourth order. 
Raigmore, Aug. 27, 1850. 


XXXIV. On the Chemical Formula of the Nitroprnssides. 
By John KvDt. 

AT the suggestion of Professor Will, I have made some 
experiments upon the nitroprnssides recently described 
by Dr. Playfair, mainly with the view of testing the simple 
and elegant formula which Dr. Playfair considers as the pro- 
bable one, although his experiments do not permit him to 

* Communicated by the Author. 

t From Liebig's Annalen, vol. Ixxiv. p. 340. 

Phil Mag. S. 3. Vol. 37. No. 250. Oct. 1850. 


290 On the Chemical Formula of the Nitroprussides. 

regard it as the expression of the analytical results. I selected 
for this purpose the soda salt, which is the most easily crystal- 
lized. The impure nitroprusside of sodium, which was ob- 
tained in solution by the saturation of the acid with carbonate 
of soda, was precipitated by the addition of sulphate of copper 
in the form of nitroprusside of copper; this was thoroughly 
washed with water, and lastly carefully decomposed by caustic 
soda. The solution of nitroprusside of sodium thus obtained 
was separated by filtration from the oxide of copper liberated, 
and evaporated at a gentle heat ; large crystals were then ob- 
tained, which I submitted to analysis. 

The iron and soda were estimated in the form of peroxide 
of iron and sulphate of soda, after the decomposition of the 
salt with concentrated sulphuric acid. 

I. 0'531 grm. gave 0-1490 grm. of peroxide of iron and 
0*2505 grm. of sulphate of soda. 

II. 0"47l grm. gave 0*1330 grm. of peroxide of iron and 
0*2223 grm. of sulphate of soda. 

Regarding the combustions, the first was made with chro- 
mate of lead, the second with peroxide of copper and oxygen 

I. 0*5 1 57 grm. gave 0*3937 grm. of carbonic acid and 0*061 
grm. of water. 

II. 0*4394 grm. gave 0*3265 grm. of carbonic acid and 
0*0526 grm. of water. 

The determination of the nitrogen was made according to 
the method of Dumas : 0298 grm. gave 74 cub. cent, of moist 
nitrogen at 57° F., and with the barometer at 28". 

I shall now compare these results with those of the com- 
position calculated according to the simplest formula given by 
Playfair, and the mean of the same chemist's analyses of the 
soda salt obtained by the same method. 

Found. Mean of 

A , ^ Playfair's 

Eq. Calc. I. 11. Mean. analyses. 

Iron ... 2 19*48 19*64 19*77 19*70 19*33 
Sodium . . 2 15*98 15-41 15*42 15*42 15*48 
Carbon . . 10 20*66 20*82 20*26 20*54 20*17 
Hydrogen . 4 1*38 1-31 1*33 1*32 1*53 

Nitrogen . 6 28*93 29*35 ... 29*35 27*78 
Oxygen . . 5 13*77 13*66 

100*00 100*00 

Playfair's more complicated formula, Fe'^ Cy'S 3NO, 5Na 

+ 10HO, requires in 100 parts, 19*33 Fe, 16*02 Na, 19*89C, 

1-38 H, and 29*00 N. It is evident, therefore, that in regard 

to the amount of soda and carbon, the analysis corresponds 

Mr. W. J. M. Rankine on the Anomaly-llnler. 291 

best with the more simple formula Fe'^ Cy^ NO, 2Na + 4<HO. 
The other elements, viz. the iron, the hydrogen and the ni- 
trogen, when calculated according to both formula;, so nearly 
coincide, that the difference cannot be ascertained with cer- 
tainty by analysis. The amount of carbon appears to me 
decisive; because, as calculated according to both formulae, it 
exhibits the greatest difference, and the quantity of carbon 
found is decidedly in favour of the more simple formula. 

XXXV. On the Anomaly -Ruler ; an Instrument to assist in the 
graphic representation of the place of a Gravitating Projectile 
in an Ellijotic Orbit. By William John Mac^uorn 
Rankine, C.E,, F.R.S.E., F.R.S.S.A. ^c* 

IT may sometimes be desirable, in lecturing on or in dis- 
cussing the motions of comets, to possess the means of 
easily and rapidly laying down on a diagram, with as much 
accuracy as the scale of the drawing will permit, the places of 
such bodies in their elliptic orbits at given instants of time. 
The instrument which I shall now describe is intended to 
facilitate this operation. 

It is simply a thin flat ruler, the form of which is repre- 
sented by the shaded figure in the drawing, and which may 
be made of any convenient size. 

The fiducial edge, from C to N, is straight. Those two 

points ought to be marked by fine transverse lines on both 

faces of the ruler. From N to I the fiducial edge has the 

* Communicated by the Author. 


292 Rev. T. P. Kirkman on Bisignal Univalent Imaginaries. 

i'ovm of the involute of the circle whose radius is CN, and 
centre C. The length of the curved portion of tlie ruler should 
be somewhat more than one-half of that of the straight pari. 

The use of this instrument is as follows: — 

Problem. — The elliptic orbit of a body, gravitating towards 
a given focus, being given, to represent on a diagrau) the place 
of the body corres})onding to a given mean anomaly. 

Solution. — About a centre C with the radius CN describe 
the circle PNQADP, and let its diameter AP be taken to 
represent the major axis of the given elliptic orbit. Let S 
represent the focus of attraction, P the perihelion, and the 
angle PCN the given mean anomaly. Apply the anomaly- 
ruler to the diagram as shown in the drawing, so that the mark 
C shall be over the centre of the circle, the mark N at the 
end of the arc of mean anomaly, and the convexity of the in- 
volute NI towards the perihelion. From the focus S draw a 
strai<rht line ST touchinnr the involute NI. Through the 
centre C draw a straight line CQ parallel to ST and on the 
same side of AP. From the point Q, where CQ cuts the 
circle, draw a straight line QB perpendicular to AP; divide 
this line by the point M in such a proportion that BQ : BM : : 
major axis : minor axis of the elliptic orbit. Then the point 
M represents the place of the body corresponding to the mean 
anomaly PCN. Q. E. I. 

The proof of this solution follows immediately from the 
31st proposition of the first book of Newton's Principia. 

If the entire ellipse PMAEP, similar to the given orbit, can 
be described with sufficient accuracy, the point M may be 
determined by the intersection of the ordinate BQ with the 
ellipse, without performing the proportional division of that line. 

It has been suggested by the Astionomer Royal for Scot- 
land, that by means of a turning-lathe a series of ellipses might 
be engraved on a plate with the same major axis, varying in 
excentricity between a circle and a straight line; and that 
impressions of this plate might be used in the graphic repre- 
sentation of cometic motions, with the aid of an anomaly-ruler 
of suitable size. 

Glasgow, August 1850. 

XXXVI. On Bisignal Univalent Imaginaries. 
By the Rev. Thomas P. Ktrkman. ilf. J.* 


F ahcdefghiklmnop be fifteen imaginaries having no linear 
relation to each other, and such that 

and also that by definition every pair of them, as m and n, 
* Communicated by the Author. 

Rev. T. P. Kirkman on Bisignal Univalent Imaginarics. 293 

possesses the property expressed by the equation ?un + nm = 0, 
we can form thiity-five triplets thus, so as to emj^loy once 
every duad that can be macle with the fifteen symbols: 

As «^^ 















— cik 

— din 











— bnp 






If we consider every triplet taken witii its sign to be equal 
to negative unity, as 

abc= —bdf= — 1, 

and to imply three equations, such as 

a = bc, b = ca, c = ab; —b = df, —d=fbi —f=bd; 
equivalent to the equations 

a= — cb, b=—ac, c=—ba; b=fd, d=bf f=idb; 

we shall find that the three equal values of each of the seven 
imaginaries, abcdefgh, deduced from the first seven triplets A, 
are all congruous with all ; and that the seven equal values of 
each of the eight imaginaries, hiklmnop, deduced from the 
twenty-eight remaining triplets B, are all congruous with all. 
Thus the two values o'i h, given by the triplets ahi and —chl^ 

h = ia = cl, 

are congruous with the values of k, given by the triplets —cik 
and aklj 

Jc = ic = la; 

for ic = la follows from ia = cL 

But if we compare the values of the first seven imaginaries, 
as given by the first seven triplets, with those deduced from 
the other twenty-eight, we find them contradictory. From 
the triplets dMi and eim, we have 

7n = dh = ei, 

de-=ih-= —hi, 
or, comparing ade, 

a= —hi; 

from bhk and —cik, we get 

k^=ibh = ic. 

291 Rev. T. P. Kirkman oji Bisigiial Univalent Imaginarics. 

or, comparing abc^ 

a = hi; 

a pair of results that can be reconciled on no less violent sup- 
position, than that the duad imaginary hi retains its value 
lahen it changes its sign : and I have shown, at page 450 of the 
thirty-third volume of this Magazine, that no one of the 
twenty-seven triplets following ahi can be admitted along with 
it, if we interpret each to express three such conditions as 
a = /z/, h = ia, i=.ah. It is there proved impossible to make 
consistently the 15x7 suppositions, such as ab = c, ac-=-—h^ 
ad=-e, &c., which are necessary to enable us to eliminate the 
duads ab, ac^ ad, &c. from the product of two pluqnaternions 
of fifteen imaginaries, 

Qj3=w + aa + ^)b + cc + ^d + ee+/f+gg + //h + a + ^-k + /l 

+ mm + ?m + oo +j'p, 

Q'lo = ^/ + ^h + ^b^ + • . +;??/. 

so as to reduce the product to the form 

Q"i.5 = w,, + «a^y + bh,, + . . . +;?P/;. 
From this consideration may be framed aproof of a celebrated 
negative, which has not yet lost its interest, although the 
question has been some time ago set at rest by a master of 
analysis, who has achieved the laborious task of establishing 
the negative by ordinary algebra. See a memoir in the 
Transactions of the Royal Irish Academy, vol. xxi., " On an 
extension of a Theorem of Euler, &c., by J. R. Young, Pro- 
fessor of Mathematics in Belfast College," a gentleman in 
whose recent and most cruel wrongs every cultivator of science 
in this empire has been bitterly insulted. The proposition 
meant is, that " Two sums each of sixteen arbitrary algebraic 
squares cannot have for their product a sum of sixteen alge- 
braic squares," 

Let it be supposed, for a moment, that they can, or that 

(w2 + a2 + b2+...+p2)(w; + a; + b,V... + p;) 

= (w,2 + a,Hb/+...+p/), 

the number of squares in each factor being sixteen. The 

w2 + a2 + b2 + ... + p2 

is the product of two pluqnaternions, 

Qi5= w + aa + 6b + . . . +;;p, 

Rev. T. P. Kirkman ow Bisignal Univalent Imaginaries. 295 


Q_,5 = w— «a— ib-. ;jp, 

Q_i5 denoting a function differing from Qj^ onl}' in the signs 
of the fifteen imaginaries abc..p, which have tiie properties 
above defined. We have then, as an equivalent form of the 
above equation, 

^15^— 15^ I5Q -15=y 15^ -15 j 

or, since Q'lsQ'-io is real, 

QloQ 15^ -15^-15 = y 15^ -15« 

The left member of our supposed equation is thus divided 
into a pair of factors, Q^Q^jand Q-isQ'-is, which differ only 
in the signs of the fifteen imaginaries; and since no such pair 
of factors can be found to produce the right member, difi'erent 
in form as to the imaginaries from Q"i5 and Q"_i5, we must 

QlS^ 15 = y 15J 
^-15^-15=^ -155 

congruous equations, considered as functions of our imagina- 
ries : but both these are proved above to be contradictory. 
The negative proposition seems thus established : but all this 
involves the petition of this other negative, that our factors Q 
cannot be formed with less than fifteen monad imaginaries. 
Why not with nine monads and six duads, as at page 453 of 
vol. xxxiii. ? 

Let us return to our refractory triplets, and try to induce 
the imaginaries to submit to the violence above hinted at. If 
in any argument it suits our convenience, for the sake of 
clearness or symmetry, to retain a term AZ, in which A is 
not infinite, and Z is zero, we may exhibit it at different points 
of the process with different signs ; for AZ is a quantity which 
changes not its value when we reverse its sign. Suppose that 
A is not a symbol of real quantity, but given in value by the 
equation A = B, when B is an imaginary having one value 
only : if there is no term in our reasoning that is affected by 
our definition of A, except AZ, we may, on reviewing our 
process, in which AZ appears with contrary signs at different 
points, conceive that the property, which the term has, of re»- 
taining its value when its sign is changed, is conferred on it by 
A, considered to be, whether affected by a positive or negative 
sign, constantly equivalent to +B: and evidently, if it facili- 
tates the establishment of relations between A and other like 
quantities, considered apart from real numbers, we may en- 
dow A by definition with the property, that its value is inde- 

296 Rev. T. P. Kirkman on Bisignal Univalent Imaginaries. 

pendent of its sign, provided that we take care in our result, 
to reduce to zero every term which is affected by the value or 
sign of A. 

Let me beg the reader's forbearance for a little while, and 
his permission to lay down, for brevity's sake, the definition 
following : — 

A bisignal univalent, or more briefly, a bisignal, is a quan- 
tity whose value is independent of its sign; and such that it 
may be employed in the same argument with contrary signs, 
and yet remain always equivalent to one defined value. 

In real aiilhiiietic there can be no bisignals, except zero 
and its reciprocal; in imaginary arithmetic we may establish 
any number, each having a value neither null nor infinite, 
if they are not suffered to affect any finite terms of our results. 

We shall then venture to define, that all the twenty-eight 
duads, /li, hk, hi, &c., made with the imaginaries hiklmnop are 
bisignal imaginaries, whose values are given by the twenty- 
eight lower triplets : and we have now the power of asserting, 
at one point of our argument, that a = hi and not =///; and 
again, at another point of the argument, that a^ih and not 
=^hi. Through all this we must retain the definition that 
hi-\-ih = 0, which is the common property of all our imagi- 
naries, by an extension of Sir W. R. Hamilton's definition of 
the three imaginaries of his quaternion theory. I am con- 
vinced that it is in vain to attempt to prove this property, at 
least in the case of those imaginaries which are not combined 
into a congruous system of seven. We are to conceive, then, 
that whenever we change for our convenience the sign of hi, 
we change by the same supposition the sign of ik ; and that 
these obliging duads are always of contrary signs. 

By this definition of the twenty-eight duads, hi, &c., we 
remove all contradiction among our triplets, z/o/?/?/ the reader 
will grant that the definition itself is not a flat contradiction. 
There is no need that we should swallow the absurdity that 
hi is of two opposite signs at once, i. e. in the same circum- 
stances : when we are about to compare, as in a preceding 
paragraph, the four triplets dhm, eim, adcsind ahi, we establish 
the proposition a = ih-- —hi ; and the result of our comparison 
agrees with this: at another moment, in other circumstances, 
when we compare together the four triplets bhk, —cik, abc and 
ahi, we first lay down that a=zhi=—ih, and our way is clear 
again. We are in a condition to bid defiance to every diffi- 
culty about the comparison of the first seven triplets with the 
lower group of twenty-eight ; and we proceed without fear to 
the formation of our sixteen functions, w^^a^^by^ Sec, which are 
to appear on the right side of the equation 

Rev. T. P. Kirkman on Bisignal Univalent Imaginaries, 297 

(w -h aa + ib + cc + . . . . -\-p\^) ( w, + aa, + ib, + cc, -|- . • • +PVi) 
= w^, + aa„ + ib^, + cc„ + r/d,, + ee„ +J t; + gg,, + /ih.^ + /i,/ 
+ Xrk,, 4- 1\„ + mm^f -f- 'ni^, + oo^^ 4-/;p,, ; 
from the congruity of which must follow at once 

(w2 + a-2 + b2 + cH... + p').(w2 + a; + b; + c;2+...+lV) 
= w/ + a,^ + b,2+...+p,;. 

The values of a and k^ for example, given by the triplets, are 

a = hc=i de =fg = {hi) = (//) = [fnn) = {op)y 
k=ila=^ bh = ic = do =pe =J'm =gn ; 

where the bisigiials are bracketed for distinction, as are also 
the terms introduced by them in the sixteen functions following: 

w^^ = w\\^— aa^ — bb^ — cc, — dd^ — ee, — ff^ — gg^ — hh^— ii^ — kk, 

— 11^ — mm^— nn^ — oo^ — PPp 
a^^=aw^+wa^ + bc, — cb^ + de^ — ed^ + fg^ — gf^+(hi^ — ih^) 

+ (kl^ — lk^) + (mn^— nm;) + (op^ — po;), 
b^, = b w, -f wb/ + ca^ — ac^ + fd^ — df^ + eg^ — ge^ + (hk, — kh^) 

+ (h^— il^) + (mo^ — omj + (pn,— np^), 
c^^=cw^ + wc, + ab, — ba, + dg/— gd, + ef, — fe^ — (hl^ — Ih^) 

— (ik^— ki,) + (mp,- pm^) + (no, -on,), 

d,,=d w, + wd, + ea^— ae, + bf, — f b, + gc, — eg, + (hm,— mh,) 

- (in,- ni,) - (ko,-ok,) + (Ip, - pi,), 

e„ = ew, + we, + ad, — da, + gb, — bg, + fc, — cf,+ (hn, — nh,) 

+ (im, — mi,) + (kp, — pk,)+(lo,-ol,), 
f„=fw, + wf, + ga,— ag, — bd, + db, + ce, — ec,— (ho, — oh,) 

g/y = g^^'/ + wg/ + ^^/-^^/ + be,— eb, + cd,-dc,+ (hp,-ph,) 

+ (io,— oi,) — (kn, — nk,) — (Im, — ml,), 
h,, = hw, + wh, + ia, — ai,4-kb, — bk, + c],— Ic +md —dm, 

+ ne,-en, + fo,-of, + pg,-gp,, 
i,^=iw,4-wi, + ah, — ha, + bl, — lb, + ck, — kc, + dn, — nd, 

+ me, — em^ + pf, — fp, + og, — go,, 
k„ = kw, + wk, + la,— al, + bh,— hb, + ic, — ci, + do,— od, 

+ pe,-ep, + fm,-mf, + gn,-ng„ 
l^,=lw, + \vl, + ak,— ka, + ib, — bi, + hc,— ch, + pd,— dp, 

+ oe,— eo, + nf,-fn, + gm, — mgp 

298 Rev. T. P. Kirkman on Bisignal Univalent Imagi?iaries, 
ni^^ = m\v^ + wm, + na^ — an^ + ob^ — bo^ + pc^— cp^ + dh^ — hd, 

+ el,-ie^ + kf^-fk, + lg,-gl^, 
ii^^ = n\v^4-\vn^+anij— ma^ + bp^— pb^ + oC/ — co, + idy— di, 

+ eh,-he, + fl-lf,+ kg^-gk^, 
o^^ = ovv^ + vvo^ + pa^ — apy + bni^ — mb^ + cn^ — nc^ + kd^ — dk^ 

+ el/-Ie/ + hf,-n)^ + gi^-ig,, 
p^^ = pw^ + vvp^ + ao^— oa^ + nb^ — bn^ + cm, — mc, + dl/— Id^ 

+ ek,-ke/ + fi^-if, + g^-lig,. 

The bracketed terms, of which there is one, and one only, 
introduced by each bisignal, must severally vanish, giving the 
seven conditions, 

h : hy=:i : i,= k : k^ = l : l, = m : m^ = n : n, = o : 0; = p : p^, 

as those which must be fidfdled in order that our results may 
be consistent with our definitions; and these seven conditions 
ought to be sufficient, if our reasoning is valid, in order that 

(w^ + a^ + b'^ + C' + d^ + e'-^+f^^gHh^ + i^ + k^ + F + m'-^ + n^ 

+ o2 + p-) 
X ( w;- + a; + b,2 + c/-^ H- d; + e,2 + f^ + g^ + h^ + i^ + k,^ + 1^2 

+ m/ + n;^ + o; + p;) 
should be identical with 

w/ + a,; + b/ + c/ + d/ + e/ + f,/ + g/ + h/ + i,^ + k,2 + l/ 
+ m/ + n/ + o/ + p,2; 
or that the product of two sums, each of sixteen algebraic 
squares, should be a sum of sixteen algebraic squares. 

That they are sufficient, is evident from inspection, and is in 
fact a known truth, discovered by Prof J. R. Young, and esta- 
blished by ocular demonstration in the memoir already I'eferred 
to; although the author gives no, account of the process by 
which he arrived at the result. Should the reader hesitate to 
accept this conclusion on the strength of my arguments, from 
a very natural suspicion that the latter are more to be admired 
for their luck than their learning, 1 trust that he will allow 
the result to be an apolog}' for the reasoning, and be lenient 
to the logic for the conclusion's sake. Is there not room to 
indulge the hope, that when the theory of these imaginaries 
is perfectly understood, as instruments of the algebra of time 
and order, what is here offered on bisignal univalents may 
amount to something better than fortunate nonsense and two 
useless words? 

Let us now consider two pluquaternions, each of twenty- 
three imaginaries, viz. the fifteen before us and the eight 

Rev. T. P. Kirkman oji BisiQiial Univalent Lnasinm-ics. 299 


h'i'k'lhn'n'o'p', all having the property //'- = i''^=... =7)'-= — 1, 
and such that 772';/ + ?/;«' = for every pair ; and ask liow many 
conditions are to be added to the seven aheady found in order 
that Q-23'Q'23=Q'W If we add to the groups of triplets A 
and B the following group, 

Ca/i'i' bh'k' -c/i'l' dh'm' eh'n' -fh'o' gh'p' 
J ak'l' -bi'l' -ci'k' -di'n' ei'm' fi'p' gi'o' 

I amhi' +bm'o' cm'p' —dk'o' eT^p^ —fk'm' —gJc'n' 
Lao'p' —bn/p' c7i'o' dl'p' eVo' fVn' —gl'm', 

we shall obtain, as before, seven congruous values of each of 
the eight h'i'k^l'm'n'dp' ; and by defining every duad imaginary 
made with these as bisignal, we shall remove all contradiction 
from the values oi abcdefg deduced from the groups AandB'. 
The equation to be satisfied, Q23 • Q'23 = Q"23» or 
( w + aa + ib + . . -f/f H-^g + //h + ^'h' + i\ + ?'i' + ^k 

+ i'k' + +jop+yp') 

X (w^ + aa^ + 6b^ + . . +/r^ + gg^ + h\^^ + ;^'h; + n^ + i\\ + /fk, 

+ /t'k/+ +J^P/+yp/) 

= w^, + aa,^ + 6b„ + . . +yir,/ +^g,; + h\\^^ + ;^'h'^^ + n^^ + i'\^l + kV^^ 

+ A"'k'^^+ +PP/,+pK, 

requires that the sixty-four duads, hh! hi' hV &c., made each 
from both groups hi...p and hH'...p'^ should be eliminated or 
otherwise disposed of. Elimination by substitution of a monad 
imaginary is impracticable ; for hk' e. g. cannot be equal to any 
of the seven abcdefg, nor to any of the eight hik . .p, nor to 
any oih'i'k . .p\ without introducing a Hnear relation between 
two of our twenty-three imaginaries, contrary to hypothesis. 
Thus the supposition hk'=f, combined with either of the ex- 
isting conditions —ho=f, m'k'=.f, would give a linear relation 
between two monads. These sixty-four duads must then per- 
force appear in the product Q.^s^o^'^ unless they are made to 
vanish by null coefficients. From our definition of h'l'^ h'k\ &c. 
as bisignals, it will follow, as befoie in the case of /i/, hk &c. 
and their coefficients, that the seven equations 

h':h'^ = i':i', = k':k'^= ..=p':p', 
must be satisfied; but there is no necessity, from these con- 
ditions, that the ratios h : h, and h' : h'^ should be equal. Now 
the duad hk' will introduce into the product of Q23 and Q'23, 
with one sign or other, the term hk', — k'h^, and no more. 
This will not vanish, unless h : h^ = k' : k'^ = h' : h', ; but does 
vanish, if the ratios h : h, and h' : h'^ are equal. As this equa- 
lity of ratios, being admitted, will cause all the sixty-four duads 
M', hi'y hk', &c. to disappear, we have our product Qaa.Q'ga 

300 Rev. T. P. Kirkman oji Bisigual Utiivaleni Imaginarics. 

of the required form Q".23; f'oni which it follows, that the pro- 
iliict of two sums each of twenty-four squares can be reduced 
algebraical!}' to a sum of twenty-four squares, if fifteen con- 
ditions are satisfied ; or that 


is a sum of twenty-four squares, if 


h, = h' 

h/ = i 

We can readily prove, by adding continually a new group 
of twenty-eight triplets made with eight new imaginaries, giving 
rise to twenty-eight new bisignal duads, that the product of 
two sums each of S{7i-{- 1) [ji > 0) algebraic squares can be re- 
duced to a sum of 8(?i+l) algebraic squares, if the given 
squares satisfy 8w — 1 conditions. Hence we have the follow- 
ing theorem : 

The product of (/■+!) sums, each ofS{n+\) algebraic squares 
{n > 0), can be reduced to a sum of 8{n+ 1) algebraic squares if 
the given roots satisfy 8nr — r assignable simple equations. 

In the case of 2"— 1 imaginaries, triplets can be formed by 
which every duad may have an equivalent monad, and this 
consistently with a law that must pervade every congruous 
system of such triplets : namely, this law, that if abc and ahi 
be two triplets, giving values a = bc=hi, both bi=ch and 
bh=iic must hold good; that is, bi and ch must be completed 
into triplets by the same imaginary vi^ and bh and ic must be 
combined with the same monad n. 

Such a system is completed for thirty-one imaginaries by 
adding to the groups ABB' the following, the signs being 
here of no importance. 



I auv 






























hm'u iin'v kni'w Im'x mm^q nm'r 

hti'v in'ti kii'x In'w 7nn'r ""»' 

ho'w io'x kohl Idv 7no's 

Jip'x ip'w hpfv Ip'n 7npH 7ip's 

717V q 













Notices respecting New Booh. 301 

The third vertical row in each of the columns in the group 
C is formed by writing under its first letter, in order, the mul- 
tipliers of that letter in the group B". The triplets, e. g. /im'u, 
hlc\ jJm'Cip'id', xm'l,.vcu; iulfill the law spoken of. If now 
under the group of triplets (B'B"C) we write two such groups 
having the same initial letters, a final group C can be added 
in the manner of C, completing the system of triplets made 
with sixty-three symbols, by all which the law in question will 
be satisfied. 

Croft Rectory, near Warrington, 
Septembers, 1850. 

XXXVII. Notices respecting New Books. 

Essay on the Theory of Attraction. By Jokk Kinnersley Smythies, 
Barrister-at-Law of the Middle Temple. 

I^'HIS paper consists of two distinct parts, geometrical and me- 
chanical : in the former, the author deserves high praise for 
his accuracy and ingenuity ; in the latter, he must bear to be told 
that he is ingenious, but not accurate. 

The geometrical part of the paper consists in a determination of 
the relation existing among the ten distances of live points in space. 
This problem was first solved by Carnot, who published a tract on 
the subject. Mr. Smythies appears not to be aware of this, by his 
not alluding to Carnot. 

The mechanical part is the asserted deduction of a principle which 
will startle every reader who is competent to be startled : it is, that 
any five material* particles have a necessary mathematical relation 
existing between their distances and central forces independently of 
their velocities. The reasoning is of the following kind. The di- 
stances between the five points being a, b, &c., the relation existing 
between them leads to a relation of the form 

/(a, da, d"-a, b, db, d^,....) = 0. 

"Where the particles are at rest, say that this becomes 

J/(ff, d''hi, b, d'"'b,....) = 0. 

We now quote from Mr. Smythies, altering the numbers of his 
equations into the letters/ and ;//. 

" The second differentials in (f) denote the whole forces, central and 
centrifugal ; and as the central force is a function of the distances only 
dependent on the positions not on the velocities of the points, the assump- 
tion that the velocities vanish destroys the centrifugal forces but does not 
alter the central. The result of that assumption, then, gives the ratios of 
the central forces when the particles begin to move from a state of rest 
when no centrifugal forces exist. But the ratios of the central forces in 

* Mr. Smythies ought to have expressed the supposition of equal par- 
tides, since he uses no ratio of masses different from unity. 

302 Boyal Socicfij. 

tliat case arc their ratios nlso when the [jarticles move witli any velocities, 
for otlierwise they would be t'linctlons of the velocities and not of the po- 
sitions only. The last etjuation (\|/-) therefore gives the necessary relation 
between the distances and central forces of five moving particles." 

On this we make no comment, nor on the conclusion that " when 
the number of spheres exceeds ten the number of equations is more 
than sufficient to determine the law of force, and no law of force is 
possible but that whicli varies directly as the distance." We shall 
merely remark, in justification of this notice, that a writer who is 
capable of the independent deduction of the relation existing among 
the distances of five points in space, is one whose errors are worth 

XXXVIII. Proceedings of Learned Societies. 

[Continued from p. 230.] 
March l-i, C\^ so-called Chylous Urine. By H. Bence Jones, 
1850. V^ iAi.D., A.M., F.R.S. &c. 

The definition given of chylous urine is, that it is urine which is 
white from the suspension of fatty matter in it. An opportunity of 
observing a case of this disease having occurred to the author, he 
was led to make the experiments described in this paper. A harness- 
maker, age 32, half-caste, who had lived in London for twelve years, 
had been passing such water for nine months. On examination of 
the water made at 2 p.m. it solidified, looking like blanc-mange in 
ten minutes. It was very feebly acid, contained fibrine, albumen, 
blood-globules and fat; specific gravity =1015. 1000 grs. of this 
urine gave — 

44<'4'2 grs. total solid residue- 
8'01 grs. total ash. 
14'03 grs. albumen. 
8-37 grs. fat. 
13*26 grs. urea and extractive matter. 
•75 gr. loss. 
955'58 grs. water. 

In order to watch the variations produced by food and exercise 
in the appearance of the urine, every time the urine was made, for 
five days and nights it was passed into bottles marked with the hour. 
From these observations, and more particularly from the third, fourth, 
and sixth days, it was evident that the fibrine and albumen appear in 
the urine when no fat is there, and that the albuminous urine occurs 
before food has been taken, and disappears during the night with 
perfect rest. Thus the fourth day, at 7^ 15™ a.m., on first getting 
up the urine contained the slightest trace of albumen. The specific 
gravity =1027; the precipitate by alcohol =0*8 gr. per 1000 grs. 

At 9'^ 50^" A.>t., just before breakfast, the urine formed a solid 
coagulum free from fatty matter, but contained a visible deposit of 

Royal Society. 303 

blood. Specific gravity =101 5*6; the precipitate by alcohol =14*1 
grs. per 1000 grs. of urine. 

At 11 A.M., the urine was chylous or white from fatty matter. 
Further experiments on the influence of rest and motion in less- 
ening or increasing the albumen in the urine previous to food are 
then given. 

On five different mornings, by rising early or late, and by col- 
lecting the precipitate fron» the urine by alcohol, the influence of 
rest and motion was determined. The author states that he could 
fix beforehand whether the urine should be albuminous or not, by 
directing the patient to get up, or to lie still. 

The patient was bled and the serum was opalescent, but did not 
clear with aether : the blood contained no excess of fat. 1000 parts 
of blood gave — 

2*63 grs. fibrine. 
159'3 grs. blood-globules. 
78*1 gi's. solids of serum. 
240*03 grs. total residue. 
759*97 grs. water. 

The urine made the same day was examined at different hours; 
that made immediately before the bleeding was quite white, and that 
made an hour and a half afterwards was very milky also. Specific 
gravity=1018. 1000 grs. of urine gave — 

56*87 grs. total residue. 
10*80 grs. total ash. 
13*95 grs. albumen. 
7*46 grs. fat. 
24*06 grs. urea, &c. 
•60 gr. loss. 
943*13 grs. water. 

The conclusions from these experiments are, — 

1. That so-called chylous urine, besides fat, may contain albumen, 
fibrine, and healthy blood-globules. 

2. That, although the fat passes off in the urine after food is taken, 
yet the albumen, fibrine arid blood-globules are thrown out before 
any food has been taken. During perfect rest the albumen ceases 
to be excreted ; and it does not appear in quantity in the urine even 
after food is taken, provided there is perfect rest. A short time after 
rising early the urine may coagulate spontaneously, although no fat 
is present ; and this may happen previous to food, when the urine is 
free from fat. 

3. Though the urine made just before and a short time after 
bleeding was as milky as it usually was at that hour of the day, yet 
the serum of the blood was not milky : it did not contain a larger 
quantity of fat than healthy blood does. 

The general results are, — 

1. That the most important changes in the urine in this disease 
take place independently of the influence of digestion. 

2. That the urine in one respect only resembles chyle, and that 

301- Roi/al Sociefj/. 

is in containing, after digestion, a large quantit}' of fat in a very fine 
state of division. Tlie su])]n)sition that tiie disease consists in an 
accumulation of fat in the blood, wiiich is thrown out by the kidneys, 
carryingwith it albumen, fibrine,blood-globules and salts, is altogether 
disproved, both by actual analyse s of the blood, and by the fre(|uent 
occurrence of a jelly-like coagulum in the urine when no white fatty 
matter can be seen to be present. 

.'5. The ilisease consists in some change in the kidney by which 
fibrine, albumen, blood-globules and salts are allowed to pass out, 
whenever the circulation through the kidney is increased ; and if at 
the same time fat is present in the blood, it escapes also into the 
urine. That this change of structure is not visible to the naked eye 
on post-mortem examination, Dr. Prout long since demonstrated ; 
and in a case of this disease which was in St. George's Hospital, and 
was examined at Plymouth, no disease of the kidney was observed. 
From the total absence of fibrinous casts of the tubes from the urine, 
it is not improbable that by the microscope a difference may be de- 
tected in the structure of the mammary processes, rather than in 
that of the cortical part of the kidneys. 

April 25. — "On the Temperature of Steam and its corresponding 
Pressure." By John Curr, Esq. Communicated by J. Scott Kussell, 
Esq., F.R.S. 

The author states that it is intended in this paper to propose a 
simple law to determine the pressure of steam corresponding to any 
given temperature, irrespectively of experiment, taking as the sole 
datum, that the vaporizing point of water under a given {pressure is 
100 degrees, that number being taken to correspond with the scale 
of Celsius; also to construct formula} in accordance therewith; and 
afterwards to compare their results with the actual experiments of the 
Academy of Sciences of Paris. He further states that the rationale 
of the subsequent formulas is expressed as follows. Let it be con- 
ceived ih&t a given quantity of water is vaporized under the condition 
that the pressure thereon is increased in the same ratio that the vo- 
lume is increased, or that at intervals of temperature 1, 2, \i, &c. the 
volume is increased the same or in equal proportions; the tempe- 
rature of the volume will be increased exactly as the square of the 
temperature indicated by the thermometer, supposing the instrument 
to be a true measure of temperature, and as the square of the vo- 
lume ; and the same of the pressure. 

Steam being generated from an indefinite quantity of water and 
confined within a limited space, as in the usual boiler, he considers 
the foregoing case is reversed; for the volume being constant, the 
action of the fire is entirely exerted in producing increased elastic 
tension of the vapour; therefore the temperature of the steam at the 
interval 1 to 2 degrees is increased inversely in the duplicate ratio 
of the ratio in the case first described ; that is, the pressure is in- 
creased directly as the square of the square, or fourth power of the 
temperature ; whence the following law. The pressure of steam 
generated in the usual steam-boiler is directly proportional to the 
fourth power of its temperature, when measured by a true scale. 

Royal Society. 305 

It being assumed that 100 degrees is the temperature of steam 
when its pressure is in equilibrium with a column of 30 inches of 
mercury, or with the pressure of one atmosphere, then F being the 
pressure in atmospheres, at any temperature t, 


A comparison is instituted between theoretic experiments of the 
Academy of Sciences and the results of this formula, from which it 
appears that the temperatures deduced from the formula are inva- 
riably in defect, tiie greatest dift'erence being '6-b\, and the least 

June 20. — " Observations on the Nebulae." By the Earl of Rosse, 
Pres.R.S., &c. Sec. 

The object of this paper is to lay before the Royal Society an ac- 
count of the progress which has been made up to the present time 
in the re-examination of Sir John Herschel's Catalogue of Nebulae 
published in the Phil. Trans, for 1833. 

Before describing any of the interesting objects the peculiar fea- 
tures of which the extraordinary powers of the telescope employed 
for their examination has brought to our knowledge, the author 
enters upon some details concerning the instrument itself. This 
telescope, which for apertures and the consequent power it possesses 
for the examination of faint details must for a considerable time, at 
least, remain unrivalled, has a clear aperture of 6 feet, with a focal 
length of 53 feet. It has hitherto been used as a Newtonian, but 
by the easy application of a little additional apparatus it may be 
conveniently worked as a Herschelian ; and the author thinks it not 
improbable that, in the further examination of the objects of most 
promise with the full light of the speculum vndiminishcd hj a second 
reflexion, some additional features of interest will come out. 

The tube reposes at its lower end upon a very massive universal 
joint of cast-iron, resting upon a pier of stonework buried in the 
ground, and it is counterpoised so that it can be moved in polar 
distance with great facility ._ The extreme range of the tube in right 
ascension at the equator is one hour, but greater as the polar distance 
diminishes. By a little subsidiary apparatus the movement of the 
telescope can be rendered almost exactly equatorial ; but up to the 
present time this apparatus has not been used, as without it, the 
movement was found to be sufficiently equatorial for such measure- 
ments as have been required. The whole mounting was planned 
especially with a view of carrying on a regular system of sweeping, 
but as yet the discovery of new nebulte has formed no part of the 
systematic work of the observatory, the known objects which re- 
quire examination being so nunuMOUs that hitherto the observers 
have been fully occupied with them. 

A clock movement M'as part of tiie original de^-ign, but as yet the 
telescope is not provided with one, and the want of it has not been 
very much felt. 

Various micrometers have been tried, but, upon the whole, the 

Phil, Macr, S. 3. Vol. 37. No. 250. Oct. 1850. X 

S()6 Royal Society. 

couinion \viro micronieter with thick linos has been found to succeed 
the best ; tor tlie faint details of the nebulae are extinguished by any 
luicrouietrical contrivance which either diminishes the light of tiie 
telescope or renders the field less dark ; and thick lines have been 
found to be visible without illumination in the darkest night. 

The telescope has two specula, one about three and a half, and 
the other rather more than four tons weight. Each is provided with 
a system of levers to afford it an equable support. Upon this 
system it was placed before it was ground, and has rested upon it 
ever since. The systems of levers with the mode of applying them 
in the support of the speculum are described in the paper, and also 
the precautions taken to guard against strain and consequent flexure 
of the metal. Notwithstanding these precautions, undoubted evi- 
dences of flexure in the speculum have occasionally shown them- 
selves. It has not, however, been found that flexure, even to the 
extent of materially disfiguring the image of a large star, interferes 
much with the action of the speculum on the faint details of nebulae^ 
although it greatly lessens its power in bringing out minute points 
of light, and in showing resolvability where, under favourable cir- 
cumstances, resolution had been previously eflTected. 

It is stated that, in the spring of 1 848, the heavier of the two 
specula, for nearly three months, performed admirably, very rarely 
exhibiting the slightest indication of flexure. It then remained in- 
active for some time before and after the solstice, and when obser- 
vations with it were again comme-iced, it was found to be in a state 
of strain. On cautiously raising it a little by screws, for the pur- 
pose of readjusting the levers, it was found that the unequal strain 
of the screws had produced permanent flexure, so that the speculum 
did not again perform well until after it had been reground. Re- 
cently an alteration has been made in the mode of supporting the 
lighter of the two specula, which now rolls freely on eighty-one 
brass balls that support it nearly equably. After referring to other 
causes of unequal action, among which the varying state of the 
atmosphere is one of the most serious, the author remarks that the 
Society will not be surprised should it be in his power at a future 
time to communicate some addit'onal particulars, even as to the 
nebulae which have been most frequently observed. 

The very beautiful sketches which illustrate the paper, are, it is 
remarked, on a very small scale, but are sufficient to convey a pretty 
accurate idea of the peculiarities of structure which have gradually 
become known. In many of the nebulae they are very remarkable, 
and seem even to indicate the presence of dynamical laws we may 
perhaps fancy to be almost within our grasp. 

On examining these sketches it will at once be remarked, as stated 
by the author, that the spiral arrangement so strongly developed in 
H. 1622, 51 Mesier, is traceable more or less distinctly in sevei'al of 
the sketches. More frequently indeed there is a nearer approach 
to a kind of irregular interrupted annular disposition of the luminous 
material, than to the regularity so striking in 51 Mesier; but it can 
scarcely be doubted that these nebulae are systems of a very similar 

Royal Society. 307 

nature, seen more or less perfectly, and variously placed with refer- 
ence to the line of sight. The author adverts to the description of 
this nebula by Mes'er, Sir William Herschel and Sir John Herschel, 
and remarks, that faking the figure given by Sir John, and placing 
it as it would be seen witli a Newtonian telescope, we shall at once 
recogni-ie the bright convolutions of the spiral which were seen by 
him as a divided ring : thus with each increase of optical power the 
strrsUire has become more complicated, and more unlike any thing 
which we could picture to ourselves as the result of any form of 
dynamical law of which we find a counterpart in our system. After 
pointing out the imporiance of measurements and the difficulty of 
taking them satisfactorily, the author states, that of a few of the 
stars with which the nebula is pretty well studded, measuremenis 
with reference to the principal nucleus were taken by his assistant 
Mr. Stoney in the spring of ISiO, and that these have been repeated 
this year during the months of April and May, and also some mea- 
sures taken from the centre of the principal nucleus to the apparent 
boundary of the spiral coils in different angles of position. A hope 
is then expressed that, as several of these stars are no doubt within 
reach of the great instruments at Pulkova and at Cambridge, U.S., 
the distinguished astronomers who have charge of them will consider 
the subject worthy of their attention. 

The spiral arrangement of 51 Mesier was detected in the spring 
of 1845, and in the following spring an arrangement, also spiral, 
but of a different character, was detected in 99 Mesier. The author 
considers that 3239 and 2370 of Herschel's ' Southern Catalogue ' 
are very probably objects of a similar character ; and as the same 
instrument does not appear to have revealed any trace of the form 
of 99 Mesier, he does not doubt that they are much more conspicu- 
ous, and therefore entertains the hope that, whenever the southern 
hemisphere shall be re-examined with instruments of great power, 
th?se two remarkable nebulae will yield some interesting result. 

The author briefly refers to the other spiral nebulae discovered 
up to the present time, which are more difficult to be seen, and to 
clusters in the exterior stars of which there appears to be a tendency 
to an arrangement in curved branches. He then passes to the re- 
gular cumular nebulse, in which, although they are perceived at once 
to be objects of a very different character, there still seems to be 
something like a connecting link. 

Among the nebulous stars two objects are stated to be well 
worthy of especial notice — No. 450 of Sir John Herschel's Catalogue, 
and i Orionis. A representation of No. 450, as seen with the six 
feet telescope, is given. It has been several times examined, but as 
yet not the slightest indication of resolvability has been seen. The 
annular form of this object was detected by Mr. Stoney when ob- 
serving alone, but Lord Rosse has since had ample opportunities of 
satisfying himself that the object has been accurately represented. 
A representation of i Orionis is likewise given. The remarkable 
feature in this object, the dark cavity not symmetrical with the star, 
wrs also discovered by Mr. Stoney when observing alone with the 


30H Intelligence and Miscellaneous Articles, 

three feet telescope. Lord Rosse has since seen it several times and 
sketched it. A small double star n,fi has similar openings, but 
are not so easily seen. These openings appear to be of the same 
character as the oj)ening within the bright stars of the trapezium of 
Orion, the stars being at the edges of the opening. Had the stars 
been situated allogetlier witiiin the o])enings, the suspicion that the 
nebula had been absorbed by the stars would perhaps have suggested 
itself more strongly. As it is, the autlior thinks we can hardly fail 
to conclude that the nebula is in some way connected with these 
briglit stars, in fact that they are equidistant, and therefore, if the 
inquiries concerning parallax should result in giving us the distances 
of these bright stars, we shall have the distance of this nebula. 

The long elliptic or lenticular nebulae are stated to be very nu- 
merous, and three sketches of remarkable objects of this class are 

In proceeding with the re-examination of Sir John Herschel's 
Catalogue, several groups of nebulae have been discovered, in some 
of which nebulous connexion has been detected between individuals 
of the group, in others not. Sketches of some have been made and 
measures taken ; but although the subject of grouped or knotted 
nebulte is considered one of deep interest, it has not yet been pro- 
ceeded with far enough to warrant entering upon it in the present 

The conclusion of the paper is occupied with remarks relating to 
each figure, in order to render the information conveyed by it more 
complete, and these are stated to be for the most part extracts 
selected from the Journal of Observations. 

XXXIX. Intelligence and Miscellajieous Articles. 


AS the results of numerous experiments, M. Baudrimont has 
arrived at the following conclusions : — 

1. That the tenacity of metals varies with their temperature. 

2. That it generally decreases, though not without exception, as 
the temperature rises. 

3. That with silver the tenacity diminishes more rapidly than the 

4. That with copper, gold, platina and palladium, it decreases less 
rapidly than the temperature. 

5. That iron presents a very peculiar and remarkable case : at 
212'' F. its tenacity is less than at 32° ; but at 392° its tenacity is 
greater than at 32°. — Comptes Rendus, Juillet 29, 1850. 


M. A. Strecker states that lactic acid, when treated with binoxide 
of lead, yields carbonic acid and aldehyd ; on the other hand, it is 
separated by heat into oxide of carbon, aldehyd and water, as 

Intelligence and Miscellaneous Articles. 309 

shown by M. Engelhardt. These reactions induced the author to 
suppose that hxctic acid might be u compound constituted of formic 
acid and hydruret of benzoyl (aldehyde bcnzoiquo). Guided by 
these ideas, M. Strecker succeeded in forming lactic acid by means of 
aldehyd and hydrocyanic acid, which is readily converted into lactic 

The following are the results of M. Strecker's experiments : — 
Aldehyd, ammonia and prussic acid, treated in aqueous solution 
by hydrochloric acid, combine and fix two equivalents of water : 
there are formed sal-ammoniac and the hydrochloric combination of 
a new substance homologous with glycocoll and leucin, which the 
author has named alanin. The following equation represents the 
formation of alanin : — 

C<H* 02-fC2NH + 2HO = C6 H- NO'. 

aldehyd alanin 

Alanin is isomeric with lactamide, nrethran and sarcosin ; it differs 
from these compounds by its proj^erties. Alanin crystallizes in 
oblique rhombic prisms ; it dissolves readily in water, but is insoluble 
in alcohol or in aether. The solution of alanin has a distinct 
sugary taste ; it has no action on litmus paper. Alanin exposed to 
a moderate heat undergoes no change ; it requires a temperature ex- 
ceeding 392° F. to sublime it, and^ this is effected without changing 
its composition. 

Alanin combines with acids, and gives a double salt with chloride 
of platina ; these combinations, the composition of which does not 
differ from the salts formed with organic bases, possess an acid re- 
action. They are readily soluble in water and in alcohol. M. 
Strecker has analysed the following compounds : — 

C6 n- NO*, NOe H ; 

C6 H' NO*, H CI ; 

2(C6H'NO\) HCl; 

2(C6 H" NO*,) H CI, 2Pt CP. 

Alanin combines also with metallic oxides, forming compounds 
soluble in water, and less soluble in alcohol. In these combinations 
the metallic oxide replaces 1 equivalent of the water of the alanin. 
The author has analysed the copper salt, crj^stallized in prisms of a 
fine blue colour (C^ H'' NO^, CuO + HO), and which loses 1 equi- 
valent of water at 248° F. ; the silver salt (C^ H'' NO^ AgO), and 
the lead salt (C^ H^ NO^, PbO, +PbO, HO). 

Alanin combines also with nitrate of silver. This compound, re- 
presented by C'' H" NO*, AgO, N0\ crystallizes in colourless rhom- 
bic tables ; it is soluble in alcohol. 

It will be observed that the properties of alanin differ much from 
those of urethan and lactamide, with which it is isomeric ; it more 
nearly resembles sarcosin, from which however it is distinguished by 
its property of combining with metallic oxides. It is therefore 
alanin, and not sarcosin, which is the homologue of glycocoll and 
leucin. By substituting valeral for aldehyd, the author hoj)es to 
obtain leucin. 

310 Litelligence and Misccllatieous Articles. 

Alanin is not acted upon by acids, nor by a boilinj^ concentrated 
solution of potash. When fused with hydrate of potash, hydrogen 
is evolved, and there are formed hydrocyanic and acetic acids, which 
remiun combined with the potash. 

If nitrous gas (NO^) be made to act upon a solution of alanin, 
much nitrogen is evolved : the solution evaporated with a gentle 
heat gives a syru]iy residue, which, treated Avith aether, yields an 
acid which was readily recognized by its reactions, and by the ele- 
mentary analysis of its zinc salt, to be lactic acid. In fact the ana- 
lysis of "this salt led to the formula C« H - 0\ ZnO + 3Aq. At 212° F. 
it loses 3 etjuivalents of water. It is thereiore common lactic acid, 
and not that found in muscular flesh. 

The formation of lactic acid in the reaction described is repre- 
sented by the equation 

C^ H" NO* + N03 = C6 H6 06 + HO -h 2N. 
alanin lactic acid 

This reaction is interesting, especially when it is considered that 
the lactic acid, the formula for which ought probably to be doubled, 
is derived from grape-sugar by a simple molecular modification. — 
Comptes Rendus, Aout 1850. 


It is generally admitted that when a salt, the oxide of which is 
insoluble, is treated with an alkaUne solution, the oxide is precipi- 
tated without redissolving, unless in its uucombined state it is so- 
luble in an excess of the alkali with which the salt containing it is 

On investigating the action of potash and soda on the arsenites, 
the author observed some facts, which, if they be not precisely 
contrary to the general law which he has cited, prove at least that 
this phsenomenon of precipitation is sometimes intimately connected 
with the nature of the salt above the precipitate ; so that, in certain 
cases, this salt may determine the solubility of the oxide. 

Thus, for example, the oxides of copper, uranium, cobalt, nickel, 
silver, mercuiy and sesquioxide of iron, being insoluble in potash and 
in soda, when these alkalies are poured into the arsenites of these 
bases, precipitation of the insoluble oxide ought merely to occur, 
M'ith the formation of arsenite of potash or soda, unaccompanied 
with any action on the oxide ; M. Reynoso has, however, found that 
the arsenites of all these oxides are completely soluble in potash, 
although in a separate state thej^ are insoluble. 

Arsenite of iron is very soluble in potash ; the solution of arsenite 
of copper is blue, and after a certain time it decomposes into prot- 
oxide of copper, w'hich precipitates, whilst the arsenite of potash 
becomes arseniate. 

The decomposition of the solution of arsenite of mercury is almost 
instantaneous. The solution of silver is colourless, and decomposes 
very slowly, precipitating silver as a black powder. This solution 

Intelligence and Miscellaneous Articles. 311 

does not precipitate with chloride of sodium ; on the contrary, chlo- 
ride of silver, which is insoluble in potash, dissolves in it very readily 
Avhen arsenite of potash is added. 

M. Reynoso took advantage of these two properties of arsenite of 
silver to effect the reduction of the salts of palladium by means of 
silver. The experiment is performed as follows : chloride of palla- 
dium, to which arsenite of potash is previously added, is poured into 
a solution of arsenite of silver in potash. A black powder is readily 
jirecipitated, which contains metallic silver and palladium. Chloride 
of platina is mu£h more readily reduced than that of palladium. 
It is to be observed that, in these reactions, arsenite of silver decom- 
poses much more quickly than when it is alone. 

The arsenites of cobalt, nickel and uranium, dissolve completely 
in potash and soda, only in the nascent state. For this purpose it 
is necessary to employ arsenite of potash with a great excess ofjjot- 
ash, and to pour this solution into a soluble salt of cobalt, nickel or 

These reactions will be readily understood, by admitting that 
arsenite of potash is capable of forming a double soluble salt with 
the compound of potash and these oxides, and that it is under this 
influence that their solution is eff^ected. When potash is made to 
act upon an insoluble salt, the oxide of which is itself soluble in an 
excess of potash, a solution can only occur on the condition of the 
formation of a soluble double salt. Thus, for example, the author 
has stated that arsenite of lead is insoluble in potash. The proof that 
these reactions depend upon the nature of the salt formed is, that 
arsenite of lead, which is insoluble in potash, is completely soluble 
in soda. 

When potash is added to an insoluble salt, it first combines with 
the acid, and the oxide set free will remain without acting upon the 
salt formed ; but if excess of potash be added, and the oxide is so- 
luble in it, then if the compound of this oxide with potash cannot 
unite with the supernatant salt, two soluble salts will be present, 
which, being able to form an insoluble salt by their decomposition, 
will regenerate the primary salts. This, however, is a very rare 
case ; for experiment has proved that almost all the salts of jDotash 
have the property of forming a soluble double salt with the oxides 
soluble in potash. 

With respect to ammonia, the author has stated the solubility 
therein of arsenite of sesquioxide of iron. 

In concluding, M. Reynoso observes that four cases of the action 
of potash on insoluble salts may occur : — 

1 . In the case of certain oxides, which, when uncombined, are 
soluble in potash, and which form soluble double salts with all the 
salts of potash, the solution may be observed under all circumstances. 

2. In some cases, uncombined oxides, which are soluble in potash, 
will form salts insoluble in potash when the acid is not such as yields 
a soluble double salt with the compound of the oxide and potash. 

3. Some other uncombined oxides, insoluble in potash, may ne- 
vertheless sometimes form a soluble double salt, and they will con- 

312 Intelligence and Miscellaneous Articles. 

sequently dissolve, when, in the nascent state, they are put into con- 
tact with potash, in the presence of the salt of potash with which 
they can combine. 

4. When the oxide is insoluble in the alkalies, it precipitates 
without redissolving, when the salt which it contains is treated with 
an excess of alkaline base. This last case happens when the oxide 
precipitated cannot form a soluble double salt. — Comptes Rendus, 
Juillct 15, 1850. 



To the Editors of the Philosophical Magazine and Journal. 

North Mall. Cork, 
Gentlemen, May 13, 1850. 

Permit me to call your attention to the following circumstance in 
connexion with elementarj' geometry ; a circumstance rendered im- 
portant merely by the fact of direct demonstration being generally 
admitted to be far superior to any indirect demonstration whatsoever*. 

Euclid, in his treatise on Geometry, proves the 40th proposition of 
the first book indirectly, which proposition I can prove directly, and 
I think in a simpler and shorter manner than his demonstration, 
thus :— ^ D 

Equal triangles (BAC and EDF) on /Y ,.' 

equal bases and on the same side, are / X,.--' 

between the same parallels. / ,.•■■" \ 

Join DA, DB and DC. The triangles /•-•• \/ 

BDC and EDF being on equal bases and ^ c e f 

between the same parallels (because they have a common altitude 
(D)), are by the 38th equal ; and as EDF is equal to ABC, BDC 
must be equal to ABC ; but these being on the same base, are by the 
39th between the same parallels. Therefore the line AD is parallel 
to BC or BF. 

Hoping this may prove worthy of insertion in your valuable 

I have the honour to be. Gentlemen, 

Your obedient Servant, 

John Hennessy, Jun. 


M. Strecker remarks, that the excellent researches of M. Wurtz 
have made known a new class of organic bases, and have thrown 
much light on the constitution of alkaloids in general. M. Hof- 
mann has lately discovered a new mode of forming these bases by 

* In Dr. Laidner's seventh edition of the Elements of Euclid, page 20, 
after showing the distinction between these two kinds of proof, he says, 
"Consequently, indirect demonstration is never used, except when no 
direct proof can he had." 

"Examples will be seen in the 14th, 19th, 25th, and 40th propositions of 
this book." 

InteUis,ence and Miscellaneous Articles. 313 


the reaction of ammonia on the chlorides and bromides of the radicals 
of the alcohols. The following is a method of preparing ethyalmin, 
which probably possesses some advantages. 

If the vapour of anhydrous sulphuric acid be absorbed by common 
ffither, suli)huric aether, properly so called, or sulphatic aether 
(C H'' O, SO') is formed, which, when water is added to it, remains 
dissolved in the excess of aether, from which it may be separated by 
spontaneous eva])oration. 

Sulphatic aether, treated with ammonia, acts like an anhydrous 
acid ; it absorbs this base, and forms an ammoniacal salt of an amided 
acid. This new salt is represented by the formula 480^, C'^ H^J 
NO'^ + NH' ; 4 equivalents of the compound aether have absorbed 2 
equivalents of ammonia, one of which has entered into the compo- 
sition of the acid. On treating this salt with carbonate of barytes 
or of lead, ammonia is evolved, and barytic or lead salts are formed 
with the new acid, named by M, Strecker ethamic acid. This acid, 
treated with a hot solution of potash, yields ethyalmin, as proved by 
the analysis of the platina salt, which gave as its composition C* H' N, 
HCl,PtCl^; there are also formed alcohol and sulphuric acid. — 
Comptes Rendiis, Aout 1850. 


It is stated by the author, in reference to the experiments on the 
above subject by M. Schonbein, that long since MM. Chevallier, 
Girardin, Graham and Weppen, had noticed some of the interesting 
phaenomena produced by it. But all these chemists made their ex- 
periments with perfectly purified animal charcoal; M. Schonbein, 
on the contrary, made use of ivory-black and coke, that is to say, of 
two varieties of carbon of complex constitution, and but little fa- 
vourable for studying the action peculiar to carbon and for distin- 
guishing it from that attributable to the foreign substances which 
accompany it. Ivory black, according to the analysis of M. Braconnot, 
contains only 79 per cent, of carbon, the remaining 21 parts being 
composed of resinous matters, sulphate and phosphate of ammonia, 
chlorides, &c., all of which are substances which can and must ever 
possess a decided influence on the results of the experiment. It is 
indeed true that the greater part of these impurities may be got rid 
of; and it would be satisfactory to know that the precaution had 
been taken, but it is not mentioned that it was so. The same may 
be said of coke, which always contains, according to the manner in 
which it has been prepared, variable proportions of sulphur and of 
sulphurets, of which it is requisite to take notice. 

M. Esprit is of opinion that the reduction of metallic solutions by 
carbon does not always occur; and he differs from M. Schonbein in 
supposing that bichloride of mercury is by its action reduced to pro- 
tochloride. It is quite true that when a cold solution, even of bi- 
chloride of mercury, is treated with powdered charcoal, no trace of 

3 1 4- Intelligence and Miscellaneous Articles. 

the bichloride is to be found in the filtered liquor : and at first it 
■would be quite natural to suppose that reduction had occurred, and 
that protochloridc of mercury would be found insoluble in the filter ; 
it is however readily shown that this is not the case, as was proved, 
according to M. Esprit, by the following experiment: — a solution 
was made of 1 grm. of sublimate in 100 grms. of distilled water, 
and this solution was treated with 20 grms. of well- washed anim?l 
charcoal : the liquor, treated with potash, hydrosulphate of ammonia 
and iodide of potassium, did not indicate the j^resence of a mercu- 
rial salt : but on washing the charcoal which had been used in the 
experiment with a mixture of alcohol and aether, sublimate Avas 
rapidly dissolved ; and in so large quantity, that when a tube was 
dipped into the solution, it gave a very distinct red precipitate with 
a solution of iodide of potassium. 

This experiment, which the author repeated several times, and 
always with the same success, induced him to think that carbon does 
not act upon metallic solutions merely as a reducing agent, nor does 
he attribute it to the mere porosity of the charcoal, but he supposes 
that the metallic salt is retained by a iieculiar force or special affinity. 
In studying the action of charcoal on metallic solutions, it is requi- 
site to employ it quite free from sulphurets and calcareous salts, the 
presence of which complicates the operation, and does not allow of 
a proper estimate of the peculiar action of the charcoal. — Journ. de 
Cliim. Med., Septembre 1850. 


It has been long known, according to the experiments of M. 
Frommherz, that tartrate of copper dissolved in a solution of potash 
is easily reduced when heated with glucose, and converted into sub- 
oxide of copper. The same author has stated that cane-sugar, which 
differs in composition from glucose, does not act upon this reagent. 
It is on these facts that M. Barreswil has founded his process for 
estimating the quantity of sugar. 

The employment of this reagent is even indicated, in several recent 
chemical works, as capable of distinguishing between cane-sugar and 

The alkaline solution of copper, emploj^ed as a test liquor, is pre- 
pared by two iiublished methods ; one by M. Barreswil, and the 
other by M. Poggiale. The first consists in dissolving with heat, in 
one-third of a litre of distilled water, 50 grammes of bitartrate of 
potash, and 40 grammes of carbonate of soda, and afterwards adding 
30 grammes of powdered crystallized sulphate of copper ; after boil- 
ing, allow the solution to cool, and lastly add 40 grammes of potash 
dissolved in one-fourth of a litre of water ; it is made up a litre and 
again boiled. The second method, proposed by M. Poggiale to de- 
termine the presence of sugar of milk, which also reduces the oxide 
of copper, like glucose, consists in dissolving in 200 grammes of 
water 10 grammes of crystalline sulphate of copper, 10 grammes of 

Ifitellisoice and Miscellaneous Articles. 315 


bitailiate of potash, and 30 g.ammes oi" potash. This solution when 
filtered is of an intense blue colour, and ought to be kept in the dark. 

The trials made with this solution proved that cane-sugar or beet- 
sugar may produce the same reaction as glucose on the alkaline 
solution of oxide of copper, according to the conditions of operating 
and the modifications which this kind of sugar may undergo by the 
influence of heat alone, or with water. 

M. Lassaigne thinks he has ascertained that glucose acts more 
readily, and at a lower temperature, on the copper reagent than 
common sugar does ; but the latter, if heated till it begins to assume 
an amber colour of less or greater depth, then acts like the former. 
In fact, an aqueous solution of glucose artificially prepared with 
starch, and containing one-fiftieth of its weight of this sugar, treated 
with the copper test at a heat of 64° to 68° F., reacts in less than 
three or four minutes, or by holding the tube inclosed in the palm 
of the hand. Under similar conditions cane-sugar produces no effect 
on the solution of copper ; but it may be kept for some time near 
212*^ without giving any appearance of reduction. By prolonging 
the time of boiling, action is at first perceived by change in the 
blue colour of the solution, slight turbidness, and the separation of a 
pulverulent yellow precipitate, which eventually becomes brick-red. 

The action of cane-sugar, not modified by heat, is slow upon the 
alkaline solution of copper ; whereas when it has been subjected to 
a more or less high temperature, the action is often as prompt as 
that of glucose on the same reagent. 

Heat, by its action on cane-sugar, ought naturally to put us on 
our guard in employing the solution of copper above mentioned for 
determining glucose in manufactured products in which it is sup- 
posed to exist. The emploj-ment of this reagent is to be suspected 
of inducing error in certain cases ; thus barley-sugar and pate de 
gomme, prepared with cane-sugar slightly caramelized by heating 
the substances which enter into their composition, acted as readily 
on the test as pure glucose. 

It has also been proved that potash, which acts in so characteristic 
a manner upon glucose, aod which has been proposed for distin- 
guishing this kind of sugar from cane or beet-sugar, often gives with 
these latter sugars reactions analogous to those developed by glucose. 
In the examination of sugars, and various alimentary or medicinal 
preparations into which they enter, the influence which heat may 
produce on these products, and the modifications which result from 
it, should be considered. — Joiirn. de Chim. Med., Juillet 1850. 


MM. Stas, Dogere and Felix Leblanc, wishing to determine the 
oxygen in carburetted hydrogen by ammoniacal protochloride of 
copper, found that this reagent dissolved a great quantity of oxide 
of carbon and even of olefiant gas. M. Leblanc, having undertaken 
the investigation of this property, obtained the following results : — 

316 Intelligence and 3Iiscellaneous Articles. 

1 . In passing a current of oxide of carbon into a solution of pro- 
tochloride of copper in hydrochloric acid, the gas was absorbed in 
considerable quantity, and with a rapidity comparable to that with 
■which carbonic acid is absorbed by potash ; but the temperature was 
comparatively but slightly raised. 

'2. The ammoniacal protochloride of copper, out of the contact of 
the air, acts in tlie same manner, and the quantity of gas absorbed 
is the same for the same quantity of copper dissolved. This solution 
becomes blue afterwards by exposure to the air, and may again serve 
to absorb oxygen. 

3. The acid protochloride of copper, saturated with oxide of car- 
bon, may be diluted even with a large quantity of water without 
precipitating protochloride of copper, as before absorption, and with- 
out any disengagement of gas. The addition of alcohol does not 
render it turbid, .^ther appears to destroy, at least partially, the 
compound which M. Leblanc has not hitherto been able to isolate. 
Ebullition or a perfect vacuum expels the gas. 

4. The fact of the absorption of oxide of carbon by the proto- 
chloride of copper appears to be of the same order as the absorption 
of nitric oxide by the salts of protoxide of iron, inasmuch as the 
absoq^tion appears to occur in definite proportions. The numbers 
approximate equal equivalents of copper and oxide of carbon. 

5. The protosalts of iron or tin do not act upon oxide of carbon. 
C. The various salts of protoxide [suboxide ?] of copper dissolved 

in ammonia absorb oxide of carbon like the protochloride of copper. 
7. Cyanogen is also absorbed by protochloride of copper; there 
is then formed a deposit of a chrome-yellow colour, which is rapidly 
modified in the air. — Journ. de Chim. Med., Juillet 1850. 


The author states that the cause is the intervention of foreign 
substances. In September 1849 he pointed out this cause in the 
variations of the angles of the prisms of sugar of gelatine ; and he 
now adduces a new fact which readily allows of verifying the influ- 
ence that a small quantity of foreign substances may exert on the 
crystalline form of bodies which are deposited in its presence. When 
a solution of chloride of cobalt containing an excess of sal-ammoniac 
is allowed to evaporate spontaneously, crystals of the last-mentioned 
salt are obtained which are more or less coloured, the angles of which 
are always near, but never 90" : the difference often exceeds 7°, and 
yet these crystals contain only 5 to 1 per cent, of chloride of co- 
balt. The same fact has been observed with respect to crystals of 
hydrochlorate of ammonia deposited in the presence of bichloride of 
platina, chloride of nickel, and also with chloride of potassium depo- 
sited under similar circumstances. — L'lnstitut, No. 852. 

Intelligence and Miscellaneoiis Articles. 317 


Some doubts having been expressed by several persons in the 
Academy with respect to the accuracy of the statements respecting 
the existence of iodine in certain pUints, the author deposited a spe- 
cimen of cress and of the iodine which he had obtained from it, and 
also of iodide of potassium procured from the same plant. 

M. Bussy also remarks that in 1839 he showed that the coal of 
Commentry contains iodine. Some portions of this coal contain 
much sulphuret of iron ; whence it happens that whilst working, 
masses often undergo a kind of slow combustion. The heat thus 
produced gives rise to thick vajjours which condense on the surface, 
and the product is found to consist of sulphuret and other arsenical 
compounds, with much sal-ammoniac, containing hydriodate of am- 
monia : at the period mentioned the author merely stated the pecu- 
liar reactions of iodine, without trying to isolate it. Not having 
any of the natural product in his possession in which he had first 
met with iodine, he had recourse to the products of the distillation 
of coal for obtaining gas ; and he found in the ammoniacal liquor a 
considerable quantity of iodine, and such as he could separate and 

The process which he adopted was to add to a certain quantity 
of the condensed water enough potash to convert the hydriodate of 
ammonia into iodide of potassium ; by evaporation to dryness and 
calcination, the tarry matter was destroyed ; and the residue being 
treated with alcohol, yielded iodide of potassium. The iodine was 
estimated by means of iodide of palladium, by the decomposition of 
which by heat iodine was obtained, of which a specimen was pre- 
sented to the Academy. 

Three kilogrammes of the condensed water of the establishment 
at the barriere of Fontainebleau yielded 0*59 gr. of iodine, nearly 0*2 
per kilogramme, or 2 ten-thousandths : iodine was also found in the 
liquor of another establishment, which renders it probable that it will 
be found in all varieties of coal. 

M. Bussy remarks that the quantity stated does not include the 
whole of the iodine contained in the coal, since a quantity remains 
in the coke, which may be obtained by incineration. 

M. Bussy observes, that the distilled product of gas-works may 
possibly be employed for the oeconomicai preparation of iodine, espe- 
cially if it could be obtained without prejudice to the separation of 
the ammoniacal salts. — L'Institvt, No. 853. 


The author, who is chemical assistant at the College of France, 
states that he has discovered bromine in the ammoniacal liquor ob- 
tained as above mentioned. He has also found the iodine previously 
mentioned by M. Bussy. — Ibid. No. 854. 

318 Intelligence atid Miscellaneous Articles. 


The author states that the antimonic, chromic, molybdic,tungstic, 
stannic, titanic, arsenic and even pliosphoric acids, are decomposed 
either with or without heat by iodide of potassium. The iodine is 
disengaged, and a salt of potash is formed. Perchloridc of iron, 
peroxide of iron, the persalts of iron and the salts of copper, act 
similai'ly on iodide of potassium. 

Bromide of potassium acts like the iodide ; but neither the chlo- 
ride of potassium or sodium is decomposed under the same circum- 
stances : the chlorides of barium, strontium, calcium and magnesium, 
and probably those of many other metals, lose chlorine when heated 
with bichromate of potash. 

M. Schonbein states also several experiments performed to show 
the deoxidizing power of powdered charcoal in different solutions. 

A solution of sesquichloride of iron is reduced to that of proto- 
chloride when agitated with powdered charcoal. Calcined lamp- 
black is more powerful than common wood-charcoal : even coke pro- 
duces the effect. 

Tlie solutions of persulphate, pernitrate and peracetate of iron are 
reduced, like the perchloride, by charcoal. The red prussiate of 
potash dissolved in water is reduced to the state of yellow prussiate 
when treated with the powder of common charcoal. 

Under the same circumstances the bichloride and pernitrate of 
mercury are reduced to protosalts of mercuiy. These reactions are 
certainly very curious ; but the interest is doubled by experiments 
undertaken to explain them. What is the effect of the charcoal on 
these reductions ? This question is not solved by M . Schonbein. 
It is difficult to believe that carbonic acid is formed ; and yet if cal- 
cined lamp-black is proper for these experiments, as stated by M. 
Schonbein, it is impossible to attribute these reductions to the hy- 
drogen which charcoal may contain. — Journ. de Pharm. , AvrW, 1850. 


To the Editors of the Philosophical Magazine and Journal. 


The Philosophical Magazine for June 1850 (vol. xxxvi. p. 489) 
contains an extract from a paper on Electro-Physiology by Sigiior 
C. Matteucci, read at the Royal Society, in which I find tlie follow- 
ing sentence: — "M. Du Bois-Reymond {Comptes Rendus) has related 
an experiment seeming to lead to the inference that section of the spinal 
marrow increases the excitability of the lumbar nerves, at least during 
a certain period of time ." 

I beg to state that I never have, either in the Comptes Rendus or 
anywhere else, described such an experiment, or any sinrUar obser- 

Meteorological Observations. 319 

vation. I cannot but express some surprise at being quoted by 
Signer Matteucci on a subject which I have not touched upon; 
whilst, on so many important occasions, this author seems to have 
been quite unacquainted with the real results I have obtained in 

I am, Gentlemen, 

Your obedient Servant, 
Berlin, 21 Carlstr. Emil nu Bois-Reymond. 

Auguot 25, 1850. 


Chiswick. — August 1. Hazy. 2. Densely overcast : slight haze : clear. 3,4. 
Fine. 5, 6. Very fine. 7. Very fine : rain at night. 8. Cloudy : slight rain. 

9. Fine. 10. Fine: drizzly. 11. Fine. 12. Fine: thunder : clear at night. 
13. Heavy clouds : very fine: lightning at night. 14. Cloudy: very fine. 15, Slight 
rain : cloudy : clear. 16. Very fine. 17, 18. Cloudy and fine. 19. Boisterous, 
with dry air: clear. 20. Fine. 21. Overcast: heavy rain: frosty at night. 

22. Clear and fine. 23,24. Cloudy : fine : clear. 25. Overcast : drizzly. 26. 
Slight rain. 27. Fine. 28. Very fine. 29. Clear and fine. 30. Very fine. 
31. Overcast. 

. Blean temperature of the month 59°'3S 

Mean temperature of Aug. 1849 62 "91 

Mean temperature of Aug. for the last twenty-four years ... 62*18 
Average amount of rain in Aug 2'41 inches. 

Boston. — Aug. 1, 2. Cloudy. 3. Fine. 4. Cloudy. 5 — 7. Fine. 8. Fine : 
rain with thunder and lightning p.m. 9. Cloudy : rain a.m. and p.m. 10. Cloudy. 
11. Fine. 12. P'ine : rain p.m. 13. Cloudy: rain a.m. and p.m. 14. Fine. 
15. Cloudy. 16. Fine. 17. Cloudy. 18. Fine. 19. Cloudy : stormy. 20. 
Fine: stormy. 21. Fine. 22. Fine: rain p.m. 23,24. Fine. 25. Cloudy: 
rain p.m. 26. Fine. 27. Cloudy : rain p.m. 28 — SO. Fine. 31. Cloudy. 

Applegarth Manse, Dunifries -shire. — Aug. 1. Slight shower at night : fine day. 
2. Slight drizzle : fine day. 3. Fair and fine, though cool. 4. Heavy rain and 
high wind. 5. Fine a.m. : rain p.m. 6. Fair and fine a.m. : shower p.m. 7. 
Fair and fine : rain p.m. 8. Rain a.m. : cleared : rain p.m. 9. Rain : cleared p.m. 

10. Rain P.M. II. Rain. 12. Rain : fine p.m. 13. Fair and fine. 14. Fair: 
sultry. 15. Warm: sultry. 16. Fair : slight drizzle. 17. Fine : slight drizzle. 
18. Wet nearly all day. 19. Shower : stormy. 20. Showers short and frequent. 
21. Fine harvest day. 22. Sltowery : hail: cool. 23. Fair till 5 I'. M. : rain 
heavy. 24. Frequent showers: hail. 25. Wet day : cleared p.m. 26. Fine 
harvest day : slight shower. 27. Heavy rain all day : flood. 28. Fine harvest 
morning: one shower. 29. Fine harvest morning : fair all day. 30. Fine har- 
vest morning. 31. Slight drizzle a.m. : cleared. 

Mean temperature of the month 55°*I 

Mean temperature of Aug. 1849 56 '7 

Mean temperature of Aug. for twenty-eight years 57 "0 

Rain (average) for twenty-three years in Aug 3"60 inches, 

Sdiuiwick Manse, Orkney. — Aug. 1. Clear : cloudy. 2. Bright : cloudy. 3. 
Showers : cloudy. 4. Rain : clear. 5. Cloudy : clear. 6. Clear. 7. Clear : 
fine : cloudy. 8. Rain; thunder-showers. 9. Cloudy: rain. 10. Fog: fine. 

11. Rain: cloudy. 12. Fine : hot : fine. 13. Fine. 14. Fine: cloudy: fine. 
15. Damp : cloudy : fine. 16. Cloudy. 17. Bright: cloudy. 18. Showers: 
cloudy. 19,20. Showers. 21. Bright : clear. 22. Bright : rain and thunder. 

23, 24. Showers. 25. Rain : drizzle. 26. Showers : drizzle : showers. 27. 
Damp : rain. 28. Showers : rain. 29. Showers. 30. Cloudy : rain. 31. 









•ui'd I 

,..-. S ..... ^' S E S .. S 


^ -t 

aJ S:' I ^ ^' W i "5 ^ &■ ^ ?J >■ 5= fe *" aJ =3 <}, > I ^' B:" &* ss' c = &' | j;' ^" 

» « 

^ 'S 

;-= =;^* ^:i i 

i^t^ -• 

^ ^' jt «■ S se I ^ c «• c jt* ^" c 

(u ^* a3 Ss S= si ^ 5J &' St 5:* aJ 6s <u e' ji ^ 3: & &* ^ ^* ^ „; fe 5: & a fe c S: 




— le* —lei ^^N ^^ ^w .Htn r^ia ^\et *h1« -^1« 

<u c t 





0^3CcX)'^>pt~-r-»■.*■.-rooc^QOOOo^a^oo■o^O'^'^-c^"aoc^ooc — 


m-^o ioc<! c^o a^cc — 0000 — < !m ■^t<Nvoa>o-.oo ooNrfcJ Odiocor-uo.- 
— (»»■^yr^l».^coo7rQoo^oocc^ol0^c^LO•^7roo^o•^oot^oooo 

O S^O^O^C^o^O^C^O^O^o^o^C^C O O C^ O\do 0^o^(j^O^O^C^O^O^O^O^O O 


2 c 



— O 

6 6 

c 01 o> 

00 — 10 
o^oo o 


— 10 

— o 

(O — o 

•-T -^ 10 

CO — c^ 

O 00 c» r-i 

C ro (M C^ 

o in CO — 
■^ r^ o IN 
r-c» CO 00 

10 Tf — 


— '*— ■ 
o — — 

c^ o o 

Ch CTs r^ 

<N coo 
C^ O 3\ 
01 CO OJ 

coo 01 

lO O — 

l^ 1^0 

rN 0~i O O O 

r^co t-- o^ o 

— — (N 

— CN d 

0^ — -T 
f^ t^o 

CO 00 

00 a\ 

O O — <N -< 

CO CO o 
lO lO o 
— <N CO 


e^co•«^•l^ot^xc^c.-(^^co'*l00t^ooo^o — (Nco'*Loot>-ooo>o — 

9 1=^ O ^ 

T 1-1 E 







XL. Remarls on an alleged proof of the ^^ Method oj" Least 
Squares" contained in a late Number of the Edinburgh Re- 
vieio. In a Letter addressed to Professor J. D. Forbes, by 

' R. L. Ellis, Esq., late Fellow of Trinity College, Cam- 

My dear Sill, 

THE review of Quetelet's " Lettres a S. A. R. le Due 
regnant de Saxe Cobourg et Golha," which appeared 
in the July Number of the Edinburgh Review, contains a new 
demonstration of the method of least squares which ought not, 
I think, to pass unnoticed. If it is correct, it is so much 
simpler than those which have hitherto been received, that it 
ought to supersede them ; and if not, the sooner its incor- 
rectness is pointed out the better. 

Some years since, in a paper published in the Cambridge 
Transactions for 1844-, I made an analysis of all the demon- 
strations, or professed demonstrations of the method of least 
squares, with which I was then acquainted, and I therefore 
read this new one with more attention than you perhaps have 
given to it. 

The reviewer gives some account of the history of the sub- 
ject, and remarks that the demonstration of the least squares 
was first attempted by Gauss, but that his proof is no proof 
at all, because it assumes that in the case of a single element 
the arithmetical mean of the observed values is in all cases the 
most probable value, "a thing to be demonstrated, not as- 
sumed." Gauss afterwards gave another demonstration, which 
is perfectly rigorous; but of this the reviewer takes no notice, 
though it is mentioned in at least one of the works on the 
* Communicated by the Author. 

Phil, Mag. S. 3. Vol. 37. No. 251 . Nov. 1850. Y 

322 Mr. R. L. Ellis on an alleged Proof of 

theory of probabilities whicli he has recommended to the 
attention ofstiulents. However, in the proof which the re- 
viewer refers to, which is contained in the tract entitled 
Theoria Moius EUiptici, Gauss undoubtedly does assume that 
the arithuH tical mean is the most probable value in the case 
of direct observations of a single element. From this assump- 
tion, he shows that the probability, that the magnitude of an 
error lies between x and x + dx, must be 


h being an indeterminate constant. It follows from this, that 
the results of the method of least squares are always the most 
probable values that can be assigned to the unknown elements. 
Without referring to the Theoria Motus, you can see the de- 
tails of Gauss's reasoning in a paper by Bessel, of which a 
translation appeared in Taylor's Scientific Memoirs. The 
reviewer is right in saying tliat Gauss was not entitled to as- 
sume that the arithmetical mean is the most probable value. 
But when he speaks of this as a thing to be proved, and not 
assumed, we are led to suppose that he believes that subsequent 
writers have actually proved it. In truth this appears, not 
only from his statements, but also from the illustrations of 
which he has made use. Thus he states that if shots are fired 
at a wafer which is afterwards removed, and we are asked to 
determine from the position of the shot-marks the most pro- 
bable position of the wafer, "the theory of probabilities affords 
a ready and precise rule, applicable not only to this but to far 
more intricate cases;" and he goes on to say that it may be 
shown that the most probable position of the wafer is the 
centre of gravity of the marks. Now this result is only then 
true when the law of probability of error, which is implied in 
Gauss's assumption, really obtains; so that, according to the 
reviewer, the demonstration of the principle of least squares 
must amount to showing that this law obtains universally; or, 
which is the same thing, that the arithmetical mean is always 
the most probable value in the case of direct observations of 
a single element. If this can be proved, it is doubtless a very 
curious conclusion; but it is at any rate certain that Laplace 
has not proved it, of whom however the reviewer asserts that 
he has given a rigorous demonstration of the principle of 
least squares. From one end of Laplace's great work to 
the other, there is nothing to justify the assertion that the 
centre of gravity of the shot-marks is the most probable 
position that can be assigned for the wafer ; that is, that the 
concurrent existence of the deviations or errors which must 

the ^^ Method of Least Squares:' 323 

have taken place if the wafer really occupied this position 
is more probable than that of those which are similarly implied 
in any other hypothesis as to its place. If you find anybody 
sceptical as to this, pray ask them to point out the passage, 
either in the introductory essay, or in the work itself, or in the 

What, then, did Laplace demonstrate? something so un- 
like this, that one is disposed to wonder how he can have been 
thus misunderstood. The method of least squares is simply a 
method for the combination of linear equations, of which the 
unknown quantities are the elt-ments to be determined ; the 
constant term of each being a direct result of observation, and 
therefore affected by an unknown error, while the coefficients 
are supposed absolutely known. 

If there are more equations than requisite, that is, more than 
elements to be determined, what is the best way of combining 
them? In the first place, they must clearly be combined by 
some system of constant multipliers, else the resulting equa- 
tions, not being linear, would generally be insoluble. This 
condition, however, though absolutely necessary in practice, 
is in no way derived from the theory of probabilities. It is a 
merely practical limitation. The question thus narrowed is 
simply to determine the system of factors to be employed for 
obtaining the value of any particular element. The factors 
must of course be such that, in the final equation, the coeffi- 
cient of this element may be unity, and those of the others 
severally equal to zero. 

These conditions being fulfilled, we get a value for the ele- 
ment in question which is affected by an unknown error, namely 
the sum of the errors of observation multiplied respectively 
by the corresponding factors. The mean arithmetical value 
of this sum may in theory at least be determined, if we know 
the law of probability of error for each observation ; and 
Laplace calls that system of factors the most advantageous 
which makes this mean value a minimum. If, however, the 
law of probability of error is unknown, the mean value of the 
error cannot be determined. Nevertheless, if the number of 
observations is very large, this mean value approximates to a 
certain limit, the form of which is independent of the law .of 
probability. The essence of Laplace's tlemonstration consists 
in its enabling us to determine this limit. When this is done, 
it may easily be shown that the most advantageous system of 
factors, those, namely, which make this limiting mean value 
of the error a minimum, will give the same value to the ele- 
ment to be determined as the system of final equations ob- 
tained by employing the method of least squares, provided 

Y 2 

324' Mr. R. L. Ellis on an alleged j)roof of 

equal positive aiul negative errors are equally probable. And 
the same is of course true with respect to the remaining ele- 
ments. Thus this system of final equations gives to each 
element a value affected by a snialler average error than any 
other linear system, if" the number of observations is suffi- 
ciently large. It nowise follows that these values are the most 
piobal)le; that is, that the errors which must have been com- 
mitted if tliese are the true values, form a combination a priori 
more probable than the errors which in like manner have been 
committed if any other set of values are the true ones. The 
most advantageous set of factors for determining any element 
depends only on the coefficients of the equations to be dis- 
cussed, and not on their constant terms, which are the direct 
result of observation. Thus these factors are determinable, 
(i priori, before the observations are made. But it is only after 
the observations have been made that the most probable values 
of the elements can be found, and then only if we know the 
Jaw of probability of error. Laplace has pointed out the 
difference between the two investigations. 

This difference, however, the reviewer does not seem to 
have apprehended. He plainly supposes that Laplace proves 
the results of the method of least scjuares to be the most pro- 
bable results, which can only be the case, as Gauss had in 
effect shown, if a special law of error obtains. He therefore 
undertakes to prove, that for all kinds of observations this is 
actually the only possible law. 

But for the supposed authority of Laplace, he would pro- 
bably have perceived that nothing can be more unlikely than 
that the errors committed in all classes of observations should 
follow the same law; and that at any rate this proposition, if 
true, could only be proved inductively, and not by andjjriori 
demonstration. For it is beyond question distinctly concei- 
vable, that different laws may exist in different classes of ob- 
servation; and that which is distinctly conceivable is a priori 
possible. So that we cannot prove it to be impossible, though 
we may be able to show empirically that it is not true. 

You will probably agree with me in thinking that a wrong 
notion of Laplace's reasoning lies at the root of the reviewer's 
new demonstration. But we now come to the demonstration 
itself. The assumption that the law of error is in all cases 
the same, is, we are told, justified by our ignorance of the 
causes on which errors of observation depenil. The law 
" must necessarily be general, and apply alike to all cases, 
since the causes of error are supposed alike unknown in all." 
Two remarks are suggested by this statement: in the first 
place, that our ignorance of the causes of error is not so great 

tJic " Method of Least Squares:' 825 

but that we have exceedingly good reason to believe that they 
operate differently in different classes of observations; and in 
the second, that mere ignorance is no ground lor any infer- 
ence whatever. Ex niliilo nihil. It cannot be that because 
we are ignorant of the matter we know somethinir about it. 
Or are we to believe that the assumption is legitimate, inas- 
much as it in a manner corresponds to and represents our 
isnorance? But then what reason have we for believinf; that 
it can lead us to conclusions which correspond to and repre- 
sent outward realities? And yet the reviewer at the conclu- 
sion of his proof asserts, that, on the long run, and exccptis 
excipieiidis, the results of observation " will be found to group 
themselves according to one invariable law." Thus the 


assumption, though " it is nothing more than the expression 
of our state of complete ignorance of the causes of error and 
their mode of action," leads us by a few steps of reasoning to 
the knowledge of a positive fact, and makes us acquainted 
with a general law, which is as independent of our knowledge 
or our ignorance as the law of gravitation. 

Let us, however, suppose it to be true that the law of error 
is always the same, and that equal positive and negative errors 
are equally probable. To determine the special form of the 
law, the reviewer employs a particular case — he supposes a 
stone to be dropt with the intention that it shall fall on a 
given mark. Deviation from this mark is error; and the pro- 
bability of an error r may be expressed by the function y(?-) 
or/(.z'^ + y^), the origin of coordinates being placed at the mark. 
It is of course supposed that equal errors in all directions are 
e(]ually probable. We have now only to determine the form 
of/. This the reviewer accomplishes in virtue of a new as- 
sumption, namely, that the observed deviation is equivalent 
to two deviations parallel respectively to the coordinate axes, 
"and is therefore a compound event of which they are the sim- 
ple constituents, therefore its probability will be the product 
of their separate probabilities. Thus tlie form of our unknown 
function comes to be determined from this condition, viz. that 
the product of such functions of two independent elements is 
equal to the same function of their sum." Or in other words, 
we have to solve the functional equation 

But it is not true that the probability of a compound event is 
the product of those of its constituents, unless the simple 
events into which we resolve it are independent of each other; 
and there is no shadow of reason for supposing that the oc- 
currence of a deviation in one direction is independent of that 

326 Mr. R. L. Ellis ofi ati alleged proof of 

of a deviation in another, whether the two directions are at 
rifjlit an<rles or not. Some notion of an analogy with the 
composition of forces probably prevented the reviewer from 
perceiving that, unless it can be shown that a deviation 7/ oc- 
curs wiih the same comparative frecjuency when w has one 
value as when it has another, we are not entitled to say tiiat 
the probability of the concurrence of two deviations x and 1/ 
is the product of the probabilities of each. Without this sub- 
sidiary proof, the rest of the demonstration comes to nothing. 
The conclusion to which it leads is in itself a rediictio ad ah~ 
surdwn. Of the above written functional equation the solution 
isf{x^^) = e""'-, in being a constant, so that the probability of 
an error of the precise magnitude .r is a finite quantity; and 
I need not point out to you that it follows from hence, that 
the probability of an error whose magnitude lies between any 
assigned limits is equal to infinity, — a result of which the in- 
terpretation must be left to the reviewer. He may have 
thought that the exponential factor is the essential part of the 

and that the others might, for the sake of simplicity, be dropt 
out. But whatever his views may have been, his conclusion 
is unintelligible. 

The demonstration may, however, be amended so as to 
avoid this difficulty, and we will suppose that the reviewer 
meant something Oifferent from what he has expi'essed. Let 
f{x'^)dx be the probability of a deviation parallel to the axis 
of abscissae, of which the magnitude lies between x and x-{-dx. 
Then J\i/'^)d^i/ is similarly the probability of a deviation parallel 
to the axis ol ordinates, and lying between j/ and 3/ +t(y. Thus 
the probability that the stone drops on the elementary area 
dxdi/, of which the corner next the origin has tor its coordi- 
nates X and ?/, seems to he J\x'^)f{if)dxdij ; and as all devia- 
tions of equal magnitude are equally probable, this probabi- 
lity must remain unchanged as long as the sum of the squares 
of X and y remains the same ; so that we have for determining 
the unknown function the equation 

of which the solution is 

and as the deviation must of necessity have some magnitude 

the " Method of Least Squares" 327 

included between positive and negative infinity, we must have 

e"'-'-dx = \. 

Hence 7n must be negative; if we call it —h'^, it is easy to 
show that A is equal to — = ; so that finally 

which is what may be called Gauss's function. 

But to this demonstration, though it leads to an intelligible 
conclusion, the original objection still applies: the probability 
that the stone drops on the elementary area dxdij is not, ge- 
nerally speaking, equal to f{x^)f{y^)d.vdj/ ; so that the equation 
for determining the form of the function, namely, 

is not legitimately established. 

To illustrate this, let zT[a:y)dxdi/ be the probability that the 
stone falls on the elementary area in question; then the con- 
dition that the probability of a deviation of given magnitude 
is constant will be expressed by 

OT(.rj/) = OT( i/.r^+j/^. 0) (A.) 

Moreover, we shall plainly have 

f{x'^)z=z / '^{pcy)dij 

Ay')^J'_ '^{xy)dx\ 
and in order that the demonstration may be valid, we must have 


^ i^G^j/) dyj _ ^ -57 {xy) dx = 'U![xy) . . . . ( B .) 

If this be true, then, and then only, equation (A.) may be re- 
placed by 


But in order that (B.) may be true, ^{xr/) must evidently be 
the product of two factors; one of them a function ofj/ only, 
and the other of .r, and the integral of each factor taken be- 
tween infinite limits must be equal to unity. Combining this 

328 On an alleged prouj of the " McUiod of' Least Squares." 
conclusion with (A.), we find that 

7 - 

i!f{xj/) = — t'-'''(-i"+r), 
and consequently 


Consequently the equation for determining the form ofy re- 
sults from a tacit predetermination of that function. 
The assumption expressed by 

is therefore either a simple mistake or n petitio j^rincipii: the 
former, if it is deduced from the general principle that the pro- 
babihty of a compound event is ecjual to the product of those 
of its elements ; the latter, if it is made to depend on the par- 
ticular form assigned io f{x-). 

After all, too, if the demonstration were right instead of 
wrong, it would not prove what is wanted. For if the law of 
probability of a deviation parallel to a fixed axis is expressed 
by the function 

which is what the amended demonstration tends to show, the 
probability that the stone falls on the area dxdy is plainly 


Transforming this to polar coordinates, and integrating from 
to 2 TT for tlie angle vector, we get Ili^e~^''''rdr for the pro- 
bability that the deviation from the mark lies between r and 
r + d}-; a result which may be verified by integrating for r 
from zero to infinity, the integral between these limits being 
equal to unity. Thus if the deviations measured parallel to 
fixed axes follow the law which the reviewer supposes to be 
universally true, the deviations from the centre or origin fol- 
low quite another; and hence it appears that his illustration 
is altogether wrong. For if 2/re~''''^rdr is the probability of 
an error lying between r and r + d); the centre of gravity of 
the shot-marks is not the most probable position of the wafer. 
So that his hypothesis is self-contradictory. 

The original source of his error was probably the analogy 
between Gauss's law, and the limiting function in Laplace's 

I am, my dear Sir, 

Most truly yours, 

Brighton, Sept. 19. R. L. Ellis. 

Phu. Mag.5:\VolIUmm. 


[ 3<29 ] 

XLI. An Account of some Thnndcr-storms mid extraordinary 
FAectrical Phanomena that occurred in the neighbourhood of 
Manchester on Tuesday the 16th of July 1850. By Peter 
Clare, F.R.A.S., Vice-President of the Literary and Phi- 
losophical Society of Manchester^. 

[With a Plate.] 
|N the 16th of July in the present year several severe 
storms of thunder, lightning, hail and rain, attended 
with fatal results, occurred in the southern part of Lancashire 
and northern part of Cheshire, which were succeeded by some 
very extraordinary electrical appearances, such as I do not 
remember to have previously noticed, although 1 have been 
an attentive observer of electrical discharges in the atmosphere 
for more than half a century. 

These storms, with one exception (which occurred in Der- 
byshire), appear to have originated in different localities, 
within a range of fifty miles from north to south, and forty 
miles from east to west; extending from the river Ribble 
below Preston in the north to the neighbourhood of Nantwich 
in the south, and from the course of the river Irwell near 
Bury in the east, to North Meols in the west. 

For several days previous to that on which the storms oc- 
curred, the weather had been generally very fine, the barometer 
varying only from 30' J 5 inches to 30 inches, giving a mean 
for the three preceding days of 30"07 inches. The thermo- 
meter for the same period, at eight o'clock in the morning, 
varied from 65 to 67degrees of Fahrenheit; at two o'clock p.m., 
from 77 to 79 degrees ; and at ten o'clock in the evening, 
I'rom Q^ to 69 degrees, giving a mean for the four days of 
70*33 degrees; whilst during the same period the wind near 
the earth blew from the north, or north-north-east, and the 
clouds during the whole time moved from east to west. 

On the morning of the 16th, previous to the commencement 
of the storms, the weather was very fine at Manchester, with 
some thin clouds floating in the atmosphere; but as the day 
advanced the clouds became more dense, although the pressure 
of the air did not vary more than the one-hundredth part of 
an inch from eight o'clock in the morning until ten o'clock in 
the evening. About two o'clock in the afternoon some dark 
clouds had formed in the north and east, and afterwards ex- 
tended towards the west; at four o'clock those in the north- 
west had become much more dense and dark, and one or two 
distant peals of thunder were heard in that direction, but with- 

* Communicated by the Author; having been read to the Literary and 
Philosophical Society, October 1, 1850. 

330 IMr. P. Clare on some Thunder-storms 

out the usual si<:;ns of an approachinir storm. It appears, 
bowevcM-, that about this time a violent storm of thuniler and 
li<rlitnin<i; hatl commenced in the lUM^hboiirhood of Bolton, 
twelve miles noith north-west of Manchester, accompanied 
with very heavy lain and large hail-stones, and continued for 
nearly two hours, exteniling westward, ami to the west-south- 
west anil north-west, for many miles; it also extended five or 
six miles to the east, as far as Bury, a distance of nine miles 
north ot Manchester; but the rain and hail were not quite in 
such profusion as at Bolton, or to the north-west of it, never- 
theless a boy and horse were killetl by the liohtning about a 
mile and a half beyond and to the north of Bury : the boy 
was about ten yeais of age, and riding on a horse with milk 
cans attached to it; and when they got to Littlewood Cross 
they were struck by the electric fluid, and both boy and horse 
killed on the spot. During the storm a house near Union 
Square, Bury, was also struck by the lightning, but not much 

At six o'clock the rain ceased at Bolton lor nearly an hour, 
after which the thunder, lightning and rain recommenced to 
the west, north-west, and east of the town, and continued for 
some time. The damage done within the borough of Bolton 
was much less than might have been expected, considering 
the severity of the storm ; yet there were not less than seven 
houses and mills struck with the lightning; but the damage 
actually done was not to any great extent, as the fires which 
it occasioned were scon subdued. The effects of the storm 
were however more appalling in a west and north-westerly 
direction, to a distance of several miles, where the rain de- 
scended in torrents, causing the water to rush down the hills 
with immense force, covering whole meadows, carrying abun- 
dance of hay with it, and overflowing the banks of rivers to a 
considerable extent, by which one of the trains was stopped at 
the Horwich station on the Bolton and Preston Railway for 
about twenty minutes. 

In the district below the Rivington Hills the water advanced 
so unexpectedly, so rapidly, and with such impetuosity, as to 
remove whole bales of cotton from the mills, and also pieces 
of cloth from the print-works, to a considerable distance. 
Other casualties also occurred, comprising the following, some 
of which are of a melancholy character. 

At Horwich the flood rose to such a height, that the water 
burst through the windows of the cotton mill of William Ben- 
nett, jun., at Wilderswood, doing damage to the amount of 
several hundred pounds; other mills in the same neighbour- 
hood also sustained considerable injury from the flood. At 

and extraordinary Electrical Phcenomena, 331 

Adlington, a colt belonging to Ralph Shaw was drowned by 
the flood. At Black rod, Joseph France, aged forty years, 
was engaged with another man in sinking a shaft at a colliery, 
when the water rushed so suddenly into it that he could not 
be got out and was drowned. 

At Burnden the head gearing of a chain belonging to a coal- 
pit of Mr. Scowcroft's was struck by the lightning and da- 
maged ; and in the same neighbourhood, a chimney-piece in 
the house of Thomas Braughton was struck and shattered. 

At West Houghton, a large stack of hay belonging to 
Thomas Woods was set on fire, but soon extinguished. 

At Adlington, the electric fluid entered a house where a 
woman and her five children were sitting, and after breaking 
a looking-glass that hung over her head, and destroying the 
chimney ornaments, it left the house without injuring any of 
the inmates. 

At Horwich, the electric fluid entered the house of Mr. 
Welsh, broke a large mirror and sundry other articles, and 
struck a boy twelve years of age, who afterwards lay in a pre- 
carious state for some time. 

At Dobhill, to the west of Bolton, a cow belonging to Peter 
Boardman was killed in a field by the lightning. 

At Lostock, Ralph Shaw had a foal killed in a field from 
the same cause. 

James Lathom, also of Lostock, had a three-years old colt 
and a horse both killed by the lightning. 

At Belmont, a cow belonging to Benjamin Helme was killed 
by the lightning on the road near to the church. 

At Hindley, a valuable cow belonging to John Battersby, 
of Castle Hill, was killed whilst grazing in a field with nine 

At Hovrocks Fold Farm, two girls, named Alice Makinson 
of Preston, and Ellen Longworth of Horwich, were sitting in 
the kitchen with four other persons, when the electric fluid 
came down the outside of the chimney, through the roof and 
the floor, and struck Alice Makinson dead on the spot: the 
fluid hit her on the shoulder, and passing down her body tore 
the sole from one of her clogs in its resistless progress. There 
were no appearances o.n the body of the other girl, Ellen 
Longworth, of having been struck by lightning, but she was 
taken out of the kitchen in a state of insensibility ; and though 
she revived a little, and was restored to consciousness, she 
only lingered until five o'clock the next morning, when she 

These instances of the destructive violence of the storm 
occurred chiefly to the north-west and west of Bolton, between" 

332 Mr. P. Clare o)i some Thunder-storms 

tliat town and Wigan, in whicli direction it seems to have 
prooressetl ; for a little before five o'clock distant thunder was 
heard towards the east and south-east of Wigan, and about 
six another storm arose to the north of the last-named town, 
which spread or extended southward, so as to unite with that 
a[)proaching from the east; and when they united, the rain 
began to descend in torrents, having more the appearance of 
the descent of a water-spout than of a shower of rain : the 
thunder and lightning were terrific; but I have not been able 
to ascertain wiiether there was any loss of life in this imme- 
diate neighbourhood, although it is reported that a person 
was killed at Wigan. 

At St. Helens, which is six or eight miles to the south-west 
of Wigan, John Rigby, a coal miner, aged ibrty-six years, 
was looking out of an upstairs window of his house during 
the thunder-storm, about seven o'clock in the evening, when 
he was struck by the electric fluid and killed on the spot: 
there was a mark on his breast, and the shoe on his right foot 
was torn to pieces. Several persons in the same house were 
knocked down, but all of them recovered. 

Robert Gore, a farm-labourer, of Marsh-side in North 
Meols, aged twenty years, was driving his master's cart home 
between six and seven o'clock the same evening, when the 
mare took fright at the noise of the thunder and ran away; 
the man and a little boy were riding in the cart at the time : 
when the master's son came up with them, he found the mare 
and cart on the ground, and Gore lying by the side of the 
cart quite dead : the horse and boy escaped. 

Evan Rimmer, a farm-servant, aged eighteen years, was 
taking shelter with four others in a stable or shed adjoining 
William Wright's farm in Moss Lane, North Meols, when 
the building was struck by the electric fluid about seven o'clock 
the same evening during the thunder-storm, and they were all 
knocked down. Rimmer was killed; the others were put to 
bed and recovered. 

In the country between St. Helens and North Meols, a 
distance of about twenty miles in a north-westerly direction, 
several persons sustained injury by the lightning; but except- 
ing the three above mentioned, no fatal cases occurred. At 
Ormskirk, a woman who was sewing was struck blind by a 
flash of lightning, but recovered her sight in a few days. 

From North Meols the storm passed northward towards 
the river Ribble and Lytham, but it does not appear that any 
damage was done there by the lightning. 

At about eight o'clock the same evening the town of War- 
rington, which is situated several miles to the south of the 

a7id extraordinary Electrical Phcctiomena. 3^3 

direction in which the storm above described had raged, was 
also visited by a violent storm of thunder and lightning; the 
lightning was intensely vivid, and the peals ot" thunder fol- 
lowed each other in rapid succession : several accidents oc- 
curred, but no fatal cases are recorded. At Sankey, a little 
to the north-west of Warrington, a stack of hay was set on 
fire by the lightning, and a large quantity burnt before the 
flames were extinguished. A flat sailing on the canal was 
also set on fire by the same cause, but the damage done was 
not extensive. This storm appears to have been limited to a 
comparatively small district. 

About six o'clock the same evening a storm of thunder and 
lightning accompanied with heavy rain commenced about ten 
miles to the west of Warrington, and proceeded in a south- 
easterly direction. After crossing the river Mersey near 
Runcorn and Weston Point, it passed up the valley of the 
river \Veaver towards Northv.ich, a town situated ten miles 
south of Warrington. At Anderton, about a mile short of 
the town, the lightning struck a stack of hay and set it on fire, 
but the torrents of rain soon extinguished it. At Witton to 
the east, and Leftwich to the south, and both immediately ad- 
joining Northwich, it appears as if a discharge of electricity 
had struck three places at one and the same time; viz. a cot- 
tage near the toll-bar in Witton was struck, but not much 
damaged; a church in Leftwich was also struck, and a quan- 
tity of stone broken and forced off" the gable-end by the light- 
ning, which passed from thence to a gutter and down a metal 
spout to the ground ; the third was a poplar-tree in Leftwich, 
which was shivei'ed at the top and down the tiunk to the 
ground. In about an hour afterwards the spire of Davenham 
Church, situatetl tvvo miles to the south, was also struck by 
the lightning ; it first came in contact with a wind-vane at the 
top of the spire, after which it passed down a copper rod 
about two inches diameter inserted through the solid stone- 
work for several yards, with a screw and nut at the bottom to 
hold the masonry together ; and when it got to the lower end 
of the metal, left it and made a large hole in the spire about 
tvvo yards long and one foot wide; it then proceeded along 
the masonry to the bottom of the spire, where it made another 
large opening in the stone-work, from whence it immediately 
entered the tower; here an iron pipe or smoke-flue on the 
outside of the tower served as a conductor for the li<ihtninsr, 
which was conveyed without injury to the building as far as 
the metal went; but where it terminated, towards the bottom 
of the tower, some damage was done to the stone-work before 
the lightning entered the ground. 

SS4 IMr. P. Clare on some Thtmder-storms 

Later in the evenin<^ a cow belonging to the Rev. Mr. 
France of Davenham was killed in Bostock Park, about two 
miles further south; and soon afterwards a barn at Winsford, 
about a mile and a half to the west of Bostock, was struck by 
the lifrhtnintr but not much damatred ; and a little later in the 
evening a cow was killed at MnishuU, a few miles south of 

The storm extended some distance further to the south and 
west, visiting in its progress Holmes Chapel, Over, Nant- 
wich, &c. 

The electrical state of the atmosphere during the progress 
of these storms must have been very much disturbed, as ma- 
nifested by the fre(]uency and intensity of the electrical dis- 
charges; whilst the torrents of rain that f(^ll for some time 
were probably caused by the currents of air in the higher part 
ol the atmosjohere being much agitated, and moving in various 
directions, thereby allowing them to mix freely, and large 
clouds to be ra})iclly generated. 

With the limited knowledge we have of the operation of 
those causes which produce thunder-storms, the following 
view may not be undeserving a little consideration. 

If we suppose that the quantity or intensity of the electric 
fluid connected or combined with each particle or atom of 
water is not the same when the atom is in a liquid as it is when 
in an aeriform state, but, like heat, abounds more when the 
atoms are in a state of vapour than when they are in a liquid 
state, and which view some experiments appear to support; 
then, whenever a quantity of vapour is suddenly condensed in 
the atmosphere, the water, whether in the state of a liquid 
mass or in innumerable drops, would probably give out elec- 
tricity, or under favourable circumstances become positively 
electrified; by this hypothesis we may account for most, if 
not all, the phaenomena that occur in thunder-storms. 

For if the currents of warm and cold air in the atmosphere 
are in a very disturbed state, moving in opposite or various 
directions, and both nearly saturated with vapour, and if 
under such circumstances they become mixed, a portion of 
the vapour in the warm air will be condensed and form clouds : 
the clouds would be electrified with an intensity proportioned 
to their density, magnitude, rapidity with which they were 
formed, and the hygrometric state of the air between them 
and the earth ; and if sufficiently electrified, would remain in 
masses separated from each other : this appearance is often 
observed in the vicinity of an electrified cloud, or previous to 
a thunder-storm. And further, as clouds are generally of 
different magnitudes and densities, the electrical power of 

and extraordinary Electrical PlicEnomena. 335 

those most intensely charged will cause the electricity of the 
sides, or portions of other clouds nearest to them, to be elec- 
trified in a different state, according to the well-known laws 
of electrical induction : and as the larger clouds increase in 
density or electrical intensity, they will discharge portions of 
their electricity to the smaller and less intensely charged 
clouds ; these again may discharge themselves to more remote 
clouds that are still more slightly charged, and thus a succes- 
sion of flashes^of lightning and peals of thunder may occur 
for some time. But if the general state of the atmosphere 
below the clouds be very damp, the superabundant electricity 
would be quietly conveyed to the earth without producing any 
electrical appearances whatever. 

In those regions of the atmosphere where clouds float or 
are formed at a considerable elevation, and where the air is 
much more rare than near the surface of the earth, the resist- 
ance to the passage of electricity through it is much less than 
near the ground, and consequently the discharges from cloud 
to cloud will be more frequent and to greater distances than 
from the clouds to the earth. 

If the clouds are rapidly (brmed and discharge their elec- 
tricity frequently to the earth, it is probable that a very large 
amount of rain will ensue; for during the time they are charged, 
the small particles of water of which they are composed will 
be repelled from each other by the diverging power of their 
electricity ; whilst the moment a discharge takes place, espe- 
cially if it be to the earth, the electricity which kept the par- 
ticles from uniting together being removed, the drops of water 
will immediately unite in in)niense quantities, and, falling to 
the earth, will suddenly increase the shower, not only in quan- 
tity but in the size of the drops, as is frequently noticed by 
attentive observers. As the different strata of air continue to 
mix, the clouds increase and again become charged with elec- 
tricity, the drops again diverge by repulsion, and the rain 
ceases to fall as copiously as it did soon after the discharge of 
electricity to the earth ; in this manner we may account for 
the occasional change during a thunder-storm, from an im- 
mense profusion to a moderate fall of rain, and vice versa. 

In a thunder-storm prevailing over a considerable extent of 
country, and w ith the clouds at a great elevation, the discharges 
of electricity may pass several miles through the air from one 
cloud to another ; in such cases an observer may have con- 
siderable difficulty to ascertain in what portion of the sky the 
lightning has prevailed; but our late eminent president. Dr. 
Dalton, has elegantly described, at page 203 of the second 
edition of his Meteorology, how the difficulty can be explained. 

336 Mr. P. Clare on some TInunler-storms 

The electrical state of the atmosphere must have been 
greatly disturbed for a much wider district than has been de- 
scribed ; but thoiiiih we iiave no account of a thunder-storm 
liaviiig occuired on the 16th of July between Bury and the 
Derbyshire Hills, yet beyond them there was a severe storm ; 
for Mr. Ransome, F.R.C.S., informs me lie was travellin<5on 
that day between Matlock and Buxton, and whilst on the 
railway, before arriving at Rowsley, they experienced a violent 
storm of thunder, lightning and rain, about five o'clock; but 
on arriving at Buxton he did not hear that the storm had visited 
that neiiihbourhood. 

In the country between Buxton and Holmes Chapel in 
Cheshire, a distance of twenty-five miles from east to west, 
and with some lofty hills to the west of Buxton, there was 
not any severe storm of thunder and lightning on that day ; 
but some sheet litihtnino: and distant thunder were noticed 
over a considerable extent of that country in the course of the 
evening, with a little rain about sixteen or eighteen miles to 
the west of Buxton. 

The storms herein described have no extraordinary features, 
except their violence and the melancholy casualties that ac- 
companied them ; but they exhibit a case of electrical disturb- 
ance deserving notice in connexion with, or immediately pre- 
ceding the very extraordinary appearances that occurred in 
the course of the same evening. 

As the evening advanced, the sheet lightning became more 
frequent and vivid at Manchester; and before nine o'clock 
the clouds in the south-south-west and west had become very 
dark, whilst those towards the south and south-east were not 
near so dense, and were separated into masses, with open 
spaces between them ; these spaces became very plainly visible 
when the sheet lightning occurred, which about this period 
was very frequent, and accompanied with distant thunder. 

From a quarter before until half-past nine some very extra- 
ordinary appearances of lightning were observed, such as I 
never before witnessed ; several flashes seeming to be almost 
continuous, or repeated at such short intervals as were scarcely 
appreciable, whilst at other times the light actually continued 
for a considerable portion of a second. 

The bright coruscations of the electric fluid, which on or- 
dinary occasions pass between one cloud and another, or be- 
tween a cloud and the earth, in a tortuous or zigzag line, on 
tliis occasion presented a great variety of forms and ramifi- 
cations towards the south and south-south-west, similar to the 
accompanying sketches, and at an elevation of from fourteen 
to twenty degrees above the horizon (see Plate I.) ; sometimes 

and cxtraordi7iary Electrical Phccnomena. 337 

they appeared branched like the roots of a tree, and occasion- 
ally with bright balls at the termination of all or some of the 
branches. These coruscations of light commenceil about 
the south-west by south, and in all cases proceeded from west 
to east, or from right to left, passing through a horizontal 
space of from eight to fourteen degrees; and at times the 
motion of the electric fluid appeared to be so slow, that its 
progress could be easily observed. 

On three or four occasions, immediately after a ray or nar- 
row line of light had passed through a horizontal space of ten 
or twelve degrees, a luminous ball of considerable size, more 
than twice the diameter of Venus when at her greatest bril- 
liancy, suddenly appeared, and moved along in the same di- 
rection as the ray of light had passed, with a progressive 
motion from right to left, as from A to B in figs. 2 and 6, 
and occupied at least the tenth of a second in its progress. 
The other appearances were of a similar character to what are 
given in the different figures, and their motion varied from a 
horizontal to a vertical direction, as n.uch as the position of 
the figures represented in the sketches. 

Some of the coruscations of the electric fluid terminated 
with a bright ball at the extremity of each branch, as in 
fig. 5 ; whilst at other times bright balls were seen at only 
two or three branches, as at fig. 7. In all cases these lumi- 
nous appearances seemed to commence from a point where 
the clouds were not dense or dark, and to proceed through 
the air to their termination without entering or being obscured 
by a cloud. 

These, or similar phsenomena, were observed by Mr. Ran- 
some and his son at Fairfield, near Buxton, in a westerly di- 
rection, about eight o'clock ; but with this difference, that the 
branches appeared to pass from left to right, whilst those I 
witnessed passed from right to left; similar appearances were 
seen by Mr. Chrimes to the north of the zenith, about a mile 
beyond Wilmslow in Cheshire, who also observed that the 
branches passed from left to right, beginning in the west and 
moving towards the north-east; and ni some cases they were 
so near the ground, that when they disappeared he thought 
tliey were in contact with the hedges, 

Edward Brooke, Esq., of Marsden House, about five miles 
to the east of Stockport, with some friends who were on a visit 
to him, also observed these remarkable coruscations, which 
he says proceeded from left to right, similar to those observed 
near Buxton and Wilmslow ; and Colonel Stott, who was of 
the party, and who had been several years resident in the 
East Indies, declared he had very frequently noticed the dis- 

Phil. Mail. S. 3. Vol. 37. No. 251. 'Nov, 1850. Z 

338 Mr. P. Clare on some Thunder-storms 

play of lightning in that part of the world, but never saw any- 
thiii<i; like the coruscations that appeared that evening. 

Mrs. Clayton, of Adlington in Cheshire, wiiose residence 
is situated three or four miles to the south ofMarsden House, 
also observed these brilliant coruscations, and likewise says 
they appeared to proceed from left to right, or in a direction 
contrary to the drawings in the Plate. 

Mr. Aklerman Shutlleworth informs me that his sister-in- 
Jaw observed these remarkable coruscations of lightning in 
the neighbourhood of Bolton, which, being twelve miles to 
the north-north-west of Manchester, gives a much wider ex- 
tent of country in which they were observed than the previous 
accounts have stated. In the extract of a letter from her 
which he has sent, she says, " I was at Bolton on the 16th of 
July, and witnessed an awful storm of thunder and lightning 
* * * * about eight a servant who was watching at an upper 
window came to say that she saw rings of fire in the sky. 
There was a large black cloud in the south-west ; behind it 
the heavens appeared to open, throwing forth sometimes 
showers of brilliant sparks or of balls of fire, sometimes circles 
of flame, sometimes fiery serpents, and at others forked light- 
ning of unusual breadth, the clouds always edged with beau- 
tiful sheet liffhtnino;." 

Mr. Joule, F. R.S., has published a highly interesting ac- 
count in the Philosophical Magazine for August, of these re- 
markable phaenomena as observed by him. He says, some 
of the coruscations passed across the zenith ; and from the 
time that elapsed between seeing them and hearing the thunder, 
he considers their general elevation to have been about three 
miles and a half: he likewise observed that the branches 
moved from right to left, similar to what I saw, as shown in 
the accompanying figures. His residence is about a mile and 
a quarter to the west-north-west of mine. He has given a 
sketch in the Magazine of the appearance observed by him, 
which terminated in more numerous branches than those I 
noticed; but though 1 did not observe any branches so much 
fimbriated at the end as he has represented, yet Mrs. Clayton, 
to whom I showed his account, saiel she saw some branches 
very much like the figure accompanying his paper, but with 
curves at the ends bent more inwards than in his figure. 

With regard to the identity of these luminous appearances 
seen by diflerent individuals, and the apparent difference in 
the direction of their motion, as stated by the observers at 
Buxton, Marsden House, Adlington and Wilmslow, com- 
pared with the account given by the observers at Manchester 
and its vicinity, it may be remarked that Marsden House is 

and extraordinary Electrical Phcenomena. 339 

to the south of east, Buxton and Adlington to the south-east, 
and Wihiislow nearly south of Manchester. Now if we sup- 
pose these coruscations to have moved from south-west to 
north-east, and some of them at no great elevation above the 
earth or distance from Manchester, they would appear to 
move from right to left at that town or its vicinity; but if the 
same were observed at Marsden House, Adlington or Wilms- 
low, they would appear to move in an opposite direction with 
regard to the spectator, or from left to right, although in both 
cases their motion would actually commence in the south-west 
and be continued towards the north-east. 

Considering the distance of Buxton from Manchester, it is 
not likely that the same coruscations would be seen at both 
places ; nor would those observed near Buxton be identical 
with those seen near Marsden House, Adlington orWilmslow, 
on account of the lofty hills intervening, and the low elevation 
of the electrical discharges seen at the latter place ; it is there- 
fore probable that these discharges of the electric fluid were 
not confined to a very limited space, but prevailed in the at- 
mosphere over a considerable district of country, and at a very 
moderate elevation ; but there is not sufficient evidence to 
enable us to determine either their height, or to what extent 
they prevailed. 

Mr. Chrimes states that he did not hear any sound as if it 
proceeded from the coruscations of light which he observed 
in the neitjhbourhood ofWilmslow; although at the same 
time he heard distant thunder in the west, but not any sound 
in the north or north-east, although that was the direction in 
which the lights were observed to pass and disappear. And 
as all parties agree that these brilliant ramifications did not 
proceed with the usual velocity of lightning, is it not probable 
that their motion was not sufficiently rapid to cause such a 
violent concussion in the air as to produce sound? 

There were no very dense clouds where the coruscations 
appeared ; but in the same direction the sky was mostly ob- 
scured with clouds of different heights, some of which, as well 
as various strata of the air, were probably in different states of 
electrification, whereby the electric fluid might be induced to 
pass from clouds positively electrified to those in a negative 
state, or to a stratum t>f air negatively electrified. In the 
passage of electricity from a body positively electrified, it fre- 
quently becomes divided into various branches, especially as 
it approaches the negative body: this is often illustrated in 
the progress of electrical discharges from the clouds to the 
earth, when they are observed to be divided into several 
branches as they approach the ground. Similar appearances 


'340 Essaij on flic Theory of Attraction. 

are often iiDiited in strong electrical discharges with a powerful 
niacliiiie, especially where the electric fluid has to be diffused 
on or anioM|^st iinperlect conductors. 

l^robably these or similar phaMiomcna are not uncommon 
in the ton iil zone, where it is said the coruscations of light- 
ning are frecjuenily seen in the sky when there are no clouds; 
but as siniihir a})j)earances are rarely, if ever, observed ni this 
neighbourhood, I iiave been inducetl to draw up the foregoing 
account in the hope that if similar pha^nomena have been no- 
ticed, some description of them may be given by other writers. 

Manchester, September 30, 1850. 

XLII. E<^sa}^ on the Theory of Attraction. J5j/ John KiN- 
xNERSLEY S-MYTHiES, Barrisfe7-at-La\i) of the Middle Temple. 

To the Editors of the Philosophical Magazine and Journal. 

3 Oakley Square, London, 
Gentlemen, October 14, 1850. 

I ADMIT that my essay noticed in your last Number con- 
tains a serious error. I now perceive that wherever <^ 
(the function of the distance, according to which the attractive 
ibice varies) occurs in an equation, the term involving it is 
multiplied by a function of the distances and angles, which is 
zero for all positions of the bodies, so that may have any 
value consistently with the equations containing it. The cor- 
rection of this error requires that sections 11, anjl 13-18 in- 
clusive, and some short relerences to them, should be cancelled; 
the remainder will be free from this error. 

Till I read your notice, I supposed that my equation be- 
tween the ten mutual distances of five points in space was 
new ; and having since referred to Carnot's memoir, I find 
that the labour 1 spent on the solution of that problem is 
not wholly lost, since my demonstration is much shorter 
and less laborious for the reader than Carnot's. When all, 
in which 1 have been anticipated or have erred, shall have 
been deducted from my essay, 1 venture to express my hope 
that something new and true will still remain. By the publi- 
cation of this short statement in your Magazine you will much 
oblige, Gentlemen, 

Your obedient Servant, 

J. K. Smythjes. 

[ oil ] 

XLIII. On the Difftisiuti of Liquids. 
Bi/ Thomas Graham, F.Ii.S., F.C\S. 

[Concluded from p. iJSl.] 

III. Diffusion of Salts of Soda. 

(1.) npHE only salts of soda which I have yet hatl an oppor- 
A tunity of diffusing in a sufficient variety of circum- 
stances are the carbonate and sulphate. These salts ajipear 
to be equidiff'usive, but to divei'ge notwithstancHng more widely 
in the solutions of the higher proportions of salt than the cor- 
responding potash salts. It is a question whether this in- 
creased divergence is not due to the less solubility of the soda 
salts, and the nearer approach consequently to their points of 
saturation in the stronger solutions. 

Table XIII. — Diffiision of Carbonate and Sulphate of Soda. 

At 6i°. 

At 37°-7 

Parts of anhydrous salt to 

100 water. 

Density of 
solution at 










Carbouate of soda 

! 2 























8 05 








Sulphate of Soda 






























The range of the thermometer during the continuance of 
the experiments at the higher temperature was from 6']:°'5 up 
to 65'' and falling again to 6i5°; the mean of all the days being 
61<°. The temperatufe pf the other series, or of the ice-box, 

342 Prof. Graham 07i the Division of Liquids. 

was 42° the first clay, 38° the second, and 37° steadily for the 
remainder of the period ; the mean being 37°*7. 
The mean results at 64° are as follows : — 

1 2. 


6| 10. 


Carbonate of soda 4-14 

Sulphate of soda 4-31 


12-22 16-88 
13-50 19-14 

Another series of experiments was made upon a 1 percent. 

solution of liie same saUs at a mean temperature of 64-°"9. Six 
phials of each solution were diffused, and the water of two 
jars afterwards evaporated together, so that the quantities 
stated are double. 

The (liff'usion product in three experiments with the sul- 
phate of soda was 4*77, 4"75 and 480 grs.; mean 4'77 grs.' 
The diffusion product in three experiments with the carbonate 
of soda was 4'61, 4'68 and 467 grs.; mean 4*65 grs. The 
difference between the carbonate and sulphate is 0'12 gr. ; it 
is less for the present proportion of 1 per cent, of salt, than 
for 2 per cent., so that the diffusion of the salts may be con- 
verging to a perfect equality in very weak solutions. One- 
half of the preceding quantities, or the mean results for a single 
diff'usion cell, are — 

Diffusion of 1 per cent, solutions at 64°-9. 

Carbonate of soda, 2-32 grs. . . 100 
Sulphate of soda, 2-38 grs. . . 102-58 

(2.) The diff'usion of the carbonate of soda was further 
compared with the nitrate of the same base, to find whether 
their times of equal diff'usion are related like those of the cor- 
responding potash salts. The mean temperature of the first 
seven days, which was the period of diff'usion for the nitrate 
of soda, was 66°-9 ; of the last three days, 65°"2; and of the 
whole period of 9*9 days occupied by the carbonate of soda, 
66°-4. The 4 per cent, solutions were employed. 

The nitrate of soda gave a diff'usion product, in three ex- 
periments, of 11-48, 11 '58 and 12-13 grs.; mean 11*73 grs. 

The carbonate of soda, in three experiments, gave 11 66, 
11-53 and 11*52 grs.; mean 11-57 grs. A slight addition 
should be made to the latter quantity to raise the diffusion 
product from 66'-4 to 66^'9. It will appear from a subsequent 
experiment that the diff'usion of the carbonate of soda in- 
creases 0*096 gr. for a rise of one degree of temperature ; 
which will give 0*05 gr. for the half degree in question. 

Prof. Graham on the Diffmion of Liquids. 343 

Brinfjing the diffusion of the twosahs to the same temperature 
ot 66"*9, we have therefore dillusecl, of — 

Nitrate of soda, in seven days, 11"73 grs. . 100 
Carbonate of soda, in 99 days, iTGS grs. . 99*06 

The difference in the quantity diffused of the two salts is only 
O'll gr., or 1 per cent., wliich is quite within the unavoidable 
errors of observation, 

(3.) The diffusion of a 2 per cent, solution of the same salts 
was repeated at the same inferior temperature of 54 '3 as with 
the salts of potash, and under the same difficulties from fluc- 
tuation of atmospheric temperature. Two water-jars were 
evaporated together, so that the results are double. 

Nitrate of soda, diffused for seven days at a mean tempera- 
ture of 54°'3, gave 10*15, 10*24 and 9*92 grs. in three expe- 
riments; mean 10*10 grs. 

Carbonate of soda, diffused for 9*9 days at a mean tempe- 
rature of 53°'4, gave 9*93, 954 and 10*10 grs. in three expe- 
riments; mean 9*86 grs. But the latter amount is to be in- 
creased by 0*09 gr. to bring it to the diffusion of 54"'3. We 
have then for the diffusion product of the two salts at the same 
temperature of 54°*3 — 

Nitrate of soda, in 7 days, 10*10 grs. . 100 
Carbonate of soda, in 9*9 days, 9*95 grs. 98*51 

The difference is again small, nameh', 0*15 gr., or 1^ per 
cent., and within the limits of unavoidable error. 

It appears therefore that the times of equal diffusion of the 
nitrate and carbonate of soda are related like those ot the ni- 
trate and carbonate of potash, or as the square root of 1 and 
2, that is, as 1 to 1*4142. 

Relation of Salts of Potash to Salts of Soda. 

It appeared probable, from many of the experiments already 
recorded, that if any relation, in the times of equal chffusibility, 
existed between the corresponding salts of potash and soda, it 
was that of the square root of 2 to the square root of 3. 1 hey 
were accordingly diffused ibr times having this ratio; namely, 
the nitrate of potash for seven days, the nitrate of soda for 
8*57325 days ; the sulphate and carbonate of potash for 9-*9 
days, and the sulphate and carbonate of soda for 12*125 days. 
If these times are rightly chosen, the eventual diffusion pro- 
ducts of all the experiments should be equal. 1 he 1 per cent, 
solution was selected, and the number of experiments simul- 
taneously made on each salt was eight or six. The liquids of 
two water-jars were evaporated together, so that each of the 

3i4 Trol'. Ciralunn un iJiC Dijjusion qj' Liquids. 

resulls in the table below represents the (lifTusion of two cells. 
These exj)eritnenis also nfi'ord another opportunity of testinj^ 
the assumed relation between the nitrates and sulphates ol the 
same base. 

Table XIV.— Solution : 1 Salt to 100 Water, at 55°-4— 56°-l. 


Time in 

of times. 
Sol. den- 

Diffusion product of two cells ir 



Exp. I. 

Exp. II. 



Nitrate of potash 









Nitrate of soda ... 









Sulphate of potash 









Sulphate of soda... 





6 94 




Carbonate of potash 









Carbonate of soda 









The range of temperature during the period of these expe- 
riments rather exceeded 3 degrees, so that they cannot be 
considered as fortunate in that respect; but still the similarity 
between the different sets of experiments, and the near equa- 
lity of their means, is very ren;arkable. The two nitrates and 
the two sulphates may be said to coincide, the extreme differ- 
ence of the means of the four salts not being quite so much as 
1 per cent. The two carbonates fall about 3'4 per cent, 
below the sulphates and nitrates, but agree periectly with each 
other, showing a uniformity in their irregularity. This de- 
viation of the carbonates would appear essential, as it has been 
observed every time they have been compared with the sul- 

The double relation between salts of potash and salts of 
soda, and between the nitrate and sulphate class of each of 
these bases, will, I believe, be allowed to acquire considerable 
additional support from this new series of observations. 

IV. Diffusion of Sulphate of Magnesia. 

In a set of preliminary experiments upon sulphate of mag- 
nesia in comparison with sulphate of potash, the 4 per cent, 
solutions of both salts were diffused for seven days at a mean 
temperature of 57°'9, with very little fluctuation, the extreme 
range being from 58°*5 to 57°'75. The sulphate of magnesia 
is taken anhydrous in all the following experiments. The 
diffusion of sulphate of potash in three cells was 9" 16, 9*22 
and 9-57 grs.; mean 9-32 grs. 

The diffusion of sulphate of magnesia in three cells was 
5'21, ^^S and 5*34 grs.; mean 5*18 grs. The diffusion, in 

Prof. Graliam oi the Dijfhsioii of Liquiils. 345 

equal times, appears here to be as 100 sulphate of potash to 
55"58 sulphate of magnesia. We know, however, wlien un- 
equally diffusible salts are diffused for equal times, that the 
diffusion of the slower is exaggerated. Consequently the dif- 
fusion of sulphate of magnesia is likely to be represented in 
excess in these experiments. 

In a second preliminary series of experiments the same 4 
per cent, solutions were diffused, the sulphate of potash for 
eight days and the sulphate of magnesia for nineteen days, 
with the view of discovering their times of equal diffusibility. 

During the first period of eight days the temperature fluc- 
tuated considerably, beginning at 54-^, falling gradually in iour 
days to 50°'5, and rising again in four days to 53°; the ave- 
rage of the whole period was 52'^'2. I'he diffusion of sulphate 
of potash from three cells was 9'36, 9*25 and 10*52 grs. ; 
mean 9*71 grs. 

During the second period of nineteen days, which included 
the first period, the mean temperature was 5^''6. The dif- 
fusion of sulphate of magnesia iVom three cells was ll'hl, 
ir6l and 1090 grs.; mean 11-44 grs. The variation in the 
amounts diffused of both salts is greater than usual, owing no 
doubt to the changes of temperature, which were iniperlectly 

Dividing the quantity of salt diffused by the number of days, 
we have of sulphate of potash 1*214 gr. diffused per day, and 
of sulphate of magnesia 0602 gr. per day ; or the latter salt 
exhibits sensibly half the diffusibility of the former in equal 
times. This suggested the trial of times for these two salts in 
the proportion ot 1 to 2, with the view of obtaining equal dif- 

(1.) A one per cent, solution of sulphate of magnesia (an- 
hydrous) was diffused for the long period of 19"8 days, at a 
mean temperature of 54°-7, in eight cells. The diffusion 
products of four pairs of cells were 7'07, 6*71, 7*07 and 7'35 
grs.; mean 7'05 grs., or for one ceil, '6'5'o grs. 

A similar solution of sulphate of potash diffused for 9*9 
days, or half the preceding period, at a mean temperature of 
55°*4, or 0°*7 higher, gave a mean product, for two cells, of 
6*79 grs., as before stated, or for one cell, of 340 grs. The 
diffusion of sulphate of potash being 100, that of sulphate of 
magnesia is therefore 103*7, a fair approximation to equality. 
(2.) In a second series of experiments upon 1 per cent, 
solutions of the same two salts, diffused in the vault for four- 
teen and seven days respectively, with a mean temperature of 
53°-8 for the sulphate of magnesia, and 54°*3 for the sulphate 
of potash, the temperature was remarkably uniform, gradually 

31:6 Prof. Graham on the Dijfiision of Liquids. 

fallino: from 55 '2 to 53 during the longer period, but without 
any injuridiis oscillation. 

Froni eight cells, evaporated two together, tiie sulphate of 
magnesia ol)taiiied was 6'] 2, 6' 12, 6*()L and G*03 grs. ; mean 
6 "OS grs., or 3'0+ grs. ibr one cell. 

The sulphate of potash gave from eight cells, in experi- 
ments already detailed, a mean result of S'S't grs. of salt for 
two cells, or 292 grs. for one cell. The diffusion is in the pro- 
portion of 100 sulphate of jiotash to 104-'ll sulphate of mag- 
nesia, the times being as 1 to 2 for the two salts respectively. 

From these two series of experiments, it appears that, at 
54°, sulphate of magnesia has nearly, if not exactly, half the 
diff"usibility of sulphate of potash, and consequently one-fourth 
of that of hydrate of potash. Or, the times of equal diff"usion 
for these three salts appear to be 1, 2 and 4-. The squares of 
these times and the solution densities are 1, 4 and 16. Hy- 
drate of potash may possibly therefore have the same relation 
to sulphate of magnesia in solution, density and diffusibility, 
that hydrogen gas has to oxygen gas. 

(3.) A two per cent, solution of sulphate of magnesia, dif- 
fused for fourteen days, gave at 53°"9, for two pairs of cells, 
9'57 and lO'OO grs. of salt, of which the mean is 9'79 grs., 
or 4'S5 grs. for one cell. 

A similar solution of sulphate of potash diffused for seven 
days gave a mean result of 4*97 grs. of salt for one cell, at 
54°'2, as already stated. The result is a diff'usion of 100 sul- 
phate of jiotash to 97*59 sulphate of magnesia. 

(4.) A four per cent, solution of sulphate of magnesia, dif- 
fused for fourteen days, gave at 53^'7, in two pairs of cells, 
18*00 and 18-20 grs. of salt; mean 18*10 grs. for two cells, 
or 9'05 grs. for a single cell. 

A similar solution of sulphate of potash, diff'used for seven 
days at 54°'2, gave a mean result of 9*30 grs. of salt for a single 
cell, as already stated. This is a diffusion of 100 sulphate of 
potash to 97*4 sulphate of magnesia. 

The diffusion of the 2 and 4 per cent, solutions of sulphate 
of magnesia is so nearly equal to the diff'usion of the same 
proportions of sulphate of potash in half the time, that they 
may be considered as supplying additional support to the 
assumed relation between the diffusibilities of these salts. 

1 may ."tld, that a 4 per cent, solution of anhydrous sulphate 
of zinc was diffused for fourteen days, simultaneously with the 
similar solution of sulphate of magnesia, and of course at the 
same temperature of 53'^*7. Two cells, evaporated two toge- 
ther, gave 17*40 and 17*36 grs. of ignited sulphate of zinc; 
mean 17*38 grs. The salt remained, after ignition, entirely 

Prof. Grail am on the Dijpision of Liquids. 347 

soluble. Tliis is a difFusion of 8"()9 grs. for one cell, while the 
sulphate of magnesia gave 9*05 grs.; or of 100 sulphate of 
zinc to 104*14' sulphate of magnesia. This result is interesting, 
as we here find two salts which are isomorphous, and of which 
the equi-diffusion is on that account in a high degree probable, 
differing between themselves so much as 4 per cent. 

Another numerous series of experiments was made at a 
considerably lower temperature, with the view of testing several 
of the same relations. The temperature in commencing the dif- 
fusion was 41°, but fell in the course of three days to 38°'8, and 
afterwards rose to 39°, from which it never varied afterwards 
more than a degree during the diff'usion of the salts of potash 
and soda. The mean temperature for their periods did not 
vary above 0°"1 or 0°*2 from 39°'7, so that it may be supposed 
the same for all these salts. For the sulphates of magnesia, 
the mean temperature was 3S°-9, or 0°*8 lower. The times 
chosen are as the square-roots of 2, 3, 6 and 16. 

Table XV.— Solutions of 1 and 2 Salt to 100 Water, at 39^-7. 




<" s 


z ■ 















15 589 






Diffusion product of two cells 
in 1 per cent, solutions, and 
one cell in 2 per cent, solutions. 



s > 



Chloride of potassium, 2 percent... 

Nitrate of soda, 2 per cent 

Chloride of sodium, 1 per cent 

Chloride of sodium, 2 per cent 

Sulphate of soda, 1 per cent 

Sulphate of soda, 2 per cent 

Sulphate of magnesia, I per cent... 
Sulphate of magnesia, 2 per cent. .. 

6-58 6-79 6-821 6-73 

6 66 6-98 679; 6-81 

6 33j 6-63 6-73 7-06| 6-69 
6-50 6-60 6-64 6-74! 6 62 
6-60' 6-561 6 56 6-50J 6 55 

6-50' 5-43! 6:33| | 642 

6 36 6-20j 6-86 6 59; 6-50 
6-42; 6-78 6-50, 6 84 663 

Several other salts were diffused in the same circumstances 
as the preceding, of which the diffusion products have been 
previously given. Of these salts, both the 1 and 2 per cent, 
solutions of nitrate of potash gave 683 in nine days, or in the 
same time as chloride of potassium in the table. The latter 
salt maintains a sensible equality of diff'usion with the present 
series at the low, as well as it was found to do at the former 
high temperattiie. Chloride of sodium is here introduced for 
the first time : it appears to be equi-diffiisive with nitrate of 
soda. If the sulphate of magnesia diffused be increased by 
007, for its lower temperature, this salt will be in close ac- 
corilance with the salts of potash and soda. 

Taking nitrate of potash 6*83, as 100, for a standard, the 

I3i8 Prol", Ciraham on the DiJJ'iisiun ()/' Liquids. 

salt which deviates most considerably is sulphate of soda, 
which lor the 1 per cent, solution is G'.^o, or 9.3'9. A low 
temperature, however, must be unfavourable to diffusion ex- 
periments, from increasing the tendency of salts to crystallize. 

In conclusion, I may sum up the results of most interest 
which this inquiry respecting licjuid diffusion has hitherto fur- 

1. I would place first the method of observing liquid dif- 
fusion. This method, although simple, appears to admit of 
sufficient exactness. It enables us to make a new class of 
observations which can be expressed in numbers, and of which 
a vast variety of substances may be the object, in fact every- 
thing soluble. Diffusion is also a property of a fundamental 
character, upon which other properties depend, like the vola- 
tility of substances ; while the number of substances which 
are soluble and therefore diffusible, appears to be much greater 
than the number of volatile bodies. 

2. The novel scale of Solution Densities, which are sug- 
gested by the different diffusibilities of salts, and to which 
alone, guided by the analogy of gaseous diffusion, we can refer 
these diffusibilities. Liquid diffusion thus supplies the den- 
sities of a new kind of molecules, but nothing more respecting 

The fact that the relations in diffusion of different sub- 
stances refer to equal weights of those substances, and not to 
their atomic weights or equivalents, is one which reaches to 
the very basis of molecular chemistry. U'he relation most 
frequently possessed is that of equality, the relation of all 
others most easily observed. In liquid diffusion we appear to 
deal no longer with chemical equivalents or the Daltonian 
atoms, but with masses even more simply related to each other 
in weight. Founding still upon the chemical atoms, we may 
suppose that they can group together in such numbers as to 
form new and larger molecules of equal weight for different 
substances, or if not of equal weight, of weights which appear 
to have a simple relation to each other. It is this new class 
of molecules which appear to play a part in solubility and 
liquid diffusion, and not the atoms of chemical combination. 

3. The formation of classes of equi-diffusive substances. 
These classes are evidently often more comprehensive than 
the isomorphous groups, although I have reason to imagine 
that they sometimes divide such groups; that while the dif- 
fusion of salts of baryta and strontia, for instance, is similar, 
the diffusion of salts of lead may be different. 

4. The separation of the whole salts (apparently) of potash 

Mr. H. J. Brooke on the Crystalline Form of Beiidantite. 349 

and of soda into two divisions, the sulphate and nitrate groups, 
which must have a clieniical si<riiificancy. The same division 
of the salts in (juestion has been niade by M. Gerhardt, on 
the ground that the nitrate class is monobasic and the sulphate 
class bibasic. 

5. The application of liquid diffusion to the separation of 
mixed salts, in natural and in artificial operations. 

6. The application of licjuid diffusion to produce chemical 

7. The assistance which a knowledge of liquid diffusion will 
afford in the investigation of endosmose. When the diffusi- 
bility of the salts in a liquid is known, the compound effect 
presented in an endosmotic experiment may be analysed, and 
the true share ot the membrane in the result be ascertained. 

But on the mere threshold of so wide a subject as liquid 
diffusion, I must postpone speculation to the determination of 
new facts and the enlargement of my data, of the present in- 
completeness of which I am fully sensible. 

XLIV. On the Crijstalline Form of Beudantite. 
Bxj H. J. Brooke, Esq., F.R.S.^^ 

IN a paper by Dr. Percy in the September Number of this 
Journal, on the chemical constitution of Beudantite, it is 
stated that its form is certainly very similar to, if not identical 
with, that of cube-ore; that Levy maintained it to be an 
obtuse rhombohedron with the vertical an^le truncated : and 
that Descloizeaux, on the other hand, asserts that the crystals 
are cubes similar in all respects to those of cube-ore from 
Cornnall. It is clear from this statement that the crystals 
examined by Descloizea.ux were different in form from those 
examined and described by Levy, which have onlij one of the 
solid angles of the supposed cube truncated, the truncating 
face being large in comparison with the size of the crystals; 
and instead of being bright, like the other faces, is of such a 
velvety dullness as scarcely to reflect any light. 

The composition seems therefore to have influenced the 
form and character of the crystals of Levy's specimen, the 
further distinction of which from those of cube-ore cannot, 
however, on account of the imperfection of the faces, be made 

* Communicated by the Author. 

[ 350 ] 

XLV. Theory of uJLt her ificat ion. ^j/ Alexander William- 
son, Professor of Practical Chemistry in the London Uni- 

WHEN sulphuric acid is brou«flu in contact with alcohol 
under certain circumstances, a new arrangement is 
effected in the elements of the alcohol, which divide into two 
groups, forming aether and water. Now it is well known that 
the process by which this change is effected may be repre- 
sented in two ways, the difference of which consists in their 
respectively selecting for starting-point a different view of the 
constitution of alcohol. According to the one view, an atom 
of alcohol weighs 23, and is made up of C'^H^'O; so that to 
form aither, two atoms of it are needed, one of which takes 
C- H"* from the other, setting free the water with which these 
elements were combined ; whereas, according to the other 
view, alcohol weighs 4:6, and contains oeiher and water. These 
are not the only points of difference which are urged ; but 
they are the most real and tangible, and their consideration is 
sufficient for our present purpose. If by any direct fact we 
could decide which of these two expressions is the correct 
one, the ground would be clear for an examination of the 
process of a-therification itself. In order to show more clearly 
the true meaning of the facts I have to adduce on this point, 
I will bring them before you in the order in which they arose. 

My object in commencing the experiments was to obtain 
new alcohols by substituting carburetted hydrogen for hy- 
drogen in a known alcohol. With this view 1 had recourse 
to an expedient, which may render valuable services on similar 
occasions. It consisted in replacing the hydrogen first by 
potassium, and acting upon the compound thus formed by the 
chloride or iodide of the carburetted hydrogen which was to 
be introduced in the place of that hydrogen. I commenced 
with common alcohol, which, after careful purification, was 
saturated with potassium, and as soon as the action had ceased, 
mixed with a portion of iodide of aethyle equivalent to the po- 
tassium used. Iodide of potassium was readily formed on the 
application of a gentle heat, and the desired substitution was 
effected ; but, to my astonishment, the compound thus formed 
had none of the properties of an alcohol — it was nothing else 
than common aether, C"* H"^ O. 

Now this result at once struck me as being inconsistent 
with the higher formula of alcohol ; for if that body contained 
twice as many atoms of oxygen as are in aether, I ought clearly 

* Comniunicated b}' the Author; having been read before the British 
Association at Edinburgh, August 3, 1850. 

Mr. A. Williamson's Theory of jEtherification. 351 

to have obtained a product containing twice as much oxygen 
as aether does. The alternative was evident; for having ob- 
tained aether by substituting C- H^ for H in alcohol, the rela- 
tive composition of the two bodies is represented by expressing 

that fact in our formula. Thus alcohol is tt O, and the 

potassium compound is K ^' ^^^ ^^ acting upon this by 
iodide of sethyle, we have 

p2 fJS p2 t-75 

^ K + C2HU = IK+ c^HsO. 

Of course the proportion between the two bodies is the only 
point upon which I here enter, and the same reasoning would 
be applicable to any mulliple of the formulae assumed. Some 
chemists may perhaps prefer doubling them in order to avoid 
the use of atoms of hydrogen, potassium, &c. ; but I have not 
felt myself justified in doing so, because that would involve 
doubling the usual formula for water; for, as I will presently 
show, water is formed in ajtherification by replacing the car- 
buretted hydrogen of alcohol by hydrogen, which, of course, 
obliges us to assume the same unity of oxygen in both. Alcohol 
is therefore water in which half the hydrogen is replaced by 
carburetted hydrogen, and aether is water in which both atoms 
of hydrogen are replaced by carburetted hydrogen : thus, 

H^' H *-'' C^tp'-'- 

This formation of aether might however be explained after 
a fashion by the other theory — by supposing the potassium 
compound to contain aether ar\d potash, which separate during 
the action of the iodide of aethyle; so that half the a;ther ob- 
tained would have been contained in that compound, and the 
other half formed by double decomposition between potash 
and iodide of aethyle : thus — 

^' K^' 0+ ^^ ^'" P=2IK + 2(C4 Hio O). 

But although the insufficiency of this explanation becomes 
evident on a little reflection, I devised a further and niore tan- 
gible method of arrivintr at a conclusion. It consisted in act- 
ing upon the potassium compound by iodide of methyle, in 
which case I should, if that compound were aether and potash, 
obtain a mixture of aether and oxide of melhvle; whereas in 
the contrary case I should obtain a body of the composition 
C^ H'^ O. Now this substance I obtained, and neither tether 
nor oxide of methyle. 

352 IVIr. A. Williamson's T/ieori/ of JEtherification. 

In this experiment the two theories cross one another, and 
mnst lead to diHcrent results; for it is evident that, in the 
first-mentioned decomposition by which aether was formed, 
the only diflicnlty in explaining the process decisively consisted 
in our inability to prove that the carburetted hydrogen intro- 
duced instead of the hydrogen did not have in the product an 
atom of oxygen to itself, but that, on the contrary, it was 
coupled with the carburetted hydrogen already contained in 
the alcohol — the two in combination with one atom of oxygen. 
It is clear that if alcohol coufain .nether and water, and the 
carburetted hydrogen in iny first experiment formed a second 
atom of a3ther by taking the place of the hydrogen of this 
water, that the process being the same in the second experi- 
ment, we should then have obtained two aetliers. Whereas if 
the formation of aether from alcohol be effected by synthesis, 
a new carburetted hydrogen being added to the one already 
contained in the alcohol, we ought to obtain the new interme- 
diate a2ther which I obtained. 

The complete description of this remarkable body, and of 
its decompositions, will form the subject of a future paper. I 
will now merely state that its boiling-point is a little above 
10° Cent.; it is possessed of a very peculiar smell, distinctly 
different from that of common aether; and, like that body, it 
is only slightly soluble in water. It is not acted upon by the 
alkali-metals at the common atmospheric temperature. 

B}' acting upon the potassium-alcohol in like manner by 
iodide of amyle, I effected a similar substitution of the ele- 
ments of that carburetted hydrogen in the place of the hy- 
drogen of alcohol, and obtained an aether boiling at 111° C, 
havins the composition C" H^^O. There is some reason to 
believe that this body is the same which Balard obtained by 
decomposition of chloride of amyle by an alcoholic solution 
of hydrated potash, and v/hich that distinguished chemist took 
for oxide of amyle. 

From the perfect analogy of properties between the known 
terms of the alcoholic series, it was to be expected that similar 
substitutions might be effected in the others; and I have ve- 
rified this by experiment. Of course the formulae of the other 
alcohols must be reduced to half, for the same reasons as that 
of common alcohol. Methylic alcohol is therefore expressed 

C IP . C^ H ' 

by the formula jj O, as common alcohol is tt O; and 

C^ H" 

in the same manner amylic alcohol is tt O, and the same 

of the higher ones. In conformity to this fact, we must be 
able to obtain the same intermediate aethers by replacing hy- 
drogen in these alcohols (methylic and amylic) by the carbii- 

Mr. A. Wiliiamsoiv's 'iheonj <^J\'Et/ic)i/i.catioii. 3.').3 

retted hydrogen of iodide of ajthvlt", as by tlie inverse process 
described above. This I have verified in the case of the three- 
carbon lether, which may be obtained incUfferently by repla- 
cing one-tbin ih of the hydrogen of niethylic alcohol by C'- 11', 
or bv replacing one-sixth of the hydrogen of common alcohol 

by CH"\ Its rational fornuda is therefore ^^ ru^- 

By acting upon the comjiound y O by iodide of amyle, 

I obtained a thhd tEthereal compound, of which the formula 

is p5 Till O. This is evidently the only one of the three new 

aethers, which, containing an even ntnnber of carbon atoms, 
might be conceived to liave been formed from one alcoiiol ; 
but when treated with monobasic acids, as liydrochloric, it 
cannot be expected to act in tlie same manner as its homoge- 

neons isomeric, the aether pg yj- Oof the three-carbon alcohol 

TT O ; but of this I will give an exact account in the paper 

above alluded to. 

My task is now to explain the process of aetherification by the 
action of sulphuric acid (SO^ H^; upon alcohol ; and in order to 
accomplish that, I must show the connexion between those sub- 
stances and the reagents used in the above-described experi- 
ments. AVith this view, I iiave merely to add to the above 
facts the acknowledged analogy of the simple and compound 
radicals in their compounds. 1 must first show how a sub- 
stance analogous to my iodide of aethyle is formed, and then 
how by double decomposition with alcohol it jiroduces aether. 
This is very easy ; for sulphovinic acid is strictly analogous 
to iodide of lethyle plus iodide of hydrogen, which we should 
obtain by replacing SQ^ in its formula by an equivalent of 
iodine; and in order to represent the formation of this sul- 
phovinic acid, which is well known to precede that of aether, 
the simplest mode is at the same time the one most free from 
hypothesis; it consists in stating the fact, that sulphuric acid 
and alcohol are transformed into sulphovinic acid and water, 
by half the hydrogen of the former changing places with the 
carburetted hydrogen of the latter : thus — 

Now from this point it is clear that the process is the same as 
in the decompositions above described ; for by this sulphovinic 
Phil. Mail. S. 3. Vol 37. No. 25 1 . Nov. 1 850, 2 A 

354 Mr. A.Williamson's Theory of JEtherification. 

acid cominn; in contact witii an atom of alcohol, it reacts ex- 
actly in the same manner as the iodide did, iorming of course 
sulphuric acid ami aether: 

(^2 J^5 SO j^ SO 

The sulphuric acid thus reproduced comes again in contact 
with alcohol, forming sulphovinic acid, which reacts as before; 
and so the process goes on continuously, as found in practice. 

We thus see that the formation of aether from alcohol is 
neither a process of simple separation, nor one of mere syn- 
thesis ; but that it consists in the substitution of one molecule 
for another, and is effected by double decomposition between 
two compounds. I therefore admit the contact theory, inas- 
much as I acknowledge the circumstance of contact as a ne- 
cessary condition of the reaction of the molecules upon one 
another. By reducing the formulae of the alcohols to one atom 
of oxj'gen, 1 also retain the equality of volumes which the con- 
tact theory insists upon between the vapours of these bodies 
and their sethers, so that aether truly contains the elements of 
olefiantgasin addition to those of alcohol in one atom. But, 
on the other hand, I attach equal importance to all the essen- 
tial facts of the chemical theory, and rest my explanation of 
the process as much upon them as upon those of the contact 
theory; for, one-sixth of the hydrogen in alcohol truly ex- 
hibits different reactions from the remaining five, and must 
therefore be contained in that compound in a different manner 
from them ; and the alternate formation and decomposition 
of sulphovinic acid is to me, as to the partisans of the chemical 
theory, the key to explaining the process of aetherification. 

Innovations in science frequently gain ground only by dis- 
placing the conceptions which preceded them, and which served 
more or less directly as their foundation ; but, if the view which 
I have here presented be considered a step in our understand- 
ing of the subject, I must beg leave to disclaim for it the title 
of innovation ; for my conclusion consists in establishing the 
connexion and showing the compatibility of views which have 
hitherto been considered contrary ; and the best possible jus- 
tification of the eminent philosophers who advocated either 
one of the two contending theories, is thus afforded by my 
reconciling their arguments with those of their equally illus- 
trious opponents. 

Before quitting the subject of aetherification, 1 would wish 
to add a few words on an application which naturally enough 

Mr. A. Williamson's Theory of Mtherification. 355 

suggests itself of the fact to which the process is here 
ascribed. 1 refer to the transfer of iioniologous molecules in 
alternately opposite directions, which, as I have endeavoured 
to show, is the cause of the continuous action of sulphuric acid 
in this remarkable process. It may naturally be asked, why 
do hydrogen and carburetted hydrogen thus continuously 
change places? It cannot be from any such circumstance as 
superior affinity of one molecule over another, for one moment 
sees reversed with a new molecule the transfer effected during 
the preceding one. Now in reflecting upon this remarkable 
fact, it strikes the mind at once that the facility of interchange 
must be greater the more close the analogy between the mo- 
lecules exchanged ; that if hydrogen and amyle can replace 
one another in a compound, hydrogen and a^thyle, which are 
more nearly allied in composition and properties, must be able 
to replace one another more easily in the same compound; 
and that the tacility of interchange of hydrogen and methyle, 
which are still more similar, will be still greater. But if this 
be true, must not the exchange of one molecule for another of 
JdeTitical properties be the most easily effected of all ? Surely 
it must, if there be any difference at all; and if so, the law of 
analogy forbids our imagining the fact to be peculiar to hy- 
drogen among substances resembling it in other respects. 
We are thus forced to admit, that, in an aggregate of mole- 
cules of an}' compound, there is an exchange constantly going 
on between the elements which are contained in it. For in- 
stance, a drop of hydrochloric acid being supposed to be made 
up of a great number of molecules of the composition CI H, 
the proposition at which we have just arrived would lead us 
to believe that each atom of hydrogen does not remain quietly 
in juxtaposition with the atom of chlorine with which it first 
imited, but, on the contrary, is constantly changing places 
with other atoms of hydrogen, or, what is the same thing, 
changing chlorine. Of course this change is not directly sen- 
sible to us, because one atom of hydrochloric acid is like 
another ; but suppose we mix with the hydrochloric acid some 
sulphate of copper (of which the component atoms are under- 
going a similar change of place), the basilous elements hy- 
drogen and copper do not limit their change of place to the 
circle of the atoms with which they were at first combined, the 
hydrogen does not merely move from one atom of chlorine to 
another, but in its turn also replaces an atom of copper, form- 
ing chloride of copper and sulphuric acid. Thus it is, that at 
any moment of time in which we examine the mixture, the 
bases are divided between the acids; and in certain cases, 
where the difference of properties of the analogous molecules 

2 A 2 

356 Mr. A. Williainsdn's Theory of JEtherification. 

is very j^rcat, it is foiiiul lliat the stroii<Ter acid and stronger 
base remain almost entirely together, leaving the weaker ones 
coml)ineil. This is well known in the case of a mixture of 
sulpluiric at.'iil ami boiax, and is a confirmation ofour funda- 
mental assumption, that the greater the ilifference of proper- 
ties, the more diflicult is the alternate interchange of one mole- 
cule for another. 

But suppose now that instead of sulphate of copper, we 
mixed sulphate of silver with our hydrochloric acid in aqueous 
solution, and that a similar division of the bases between the 
acids established itself in the first moment, lorming four com- 
pounds, SCH^ SO-^Ag^ CIH, ClAg; it is clear that this 
last-mentioned compound, being insoluble in water, must, on 
its formation, separate out and remove from the circle of de- 
compositions which solubility established. But of course the 
three compounds remaining in solution continue the exchange 
of their component parts, and give rise successively to new 
portions of chloride of silver, until as much of that compound 
is precipitated as the liquid contained equivalents of its com- 
ponent })arts, a very small quantity remaining in solution and 
in the circle of decompositions. 

8uch is the general process of chemical decomposition. 
Of course a compound is removed as effectually from the circle 
of decompositions by possessing the gaseous form under the 
circumstances of the experiment, or even by being a liquid 
insoluble in the menstruum. I believe this explanation coin- 
cides in its second jiart with the one proposed many years ago 
by Berthollet; but not making use of the atomic hypothesis, 
upon which my explanation is based, that eminent philosopher 
went no farther back than the division of the acids between 
the bases on the mixture of salts, a fact which I have here 
deduced from the motion of atoms. It is well known that the 
general fact upon which Berthollet founded his view is denied 
by some eminent chemists of the present day ; but I believe 
the instances which they adduce are only apparent exceptions 
to the law, and will on further examination be found to afford 
additional confirmation of the truth of the great Savoysien's 
conception, as i have shown in the case of boracic and sul- 
phuric acids. 

In using the atomic theory, chemists have added to it of 
late years an unsafe, and, as I think, an unwarrantable hy- 
pothesis, namely that the atoms are in a state of rest. Now 
this hypothesis I discard, and reason upon the broader basis 
of atomic motion. 

[ 357 ] 

XL VI. Account of a remarkable Meteor, seen December J 9, 
1849. By Professor J. D. Forbes*. 

ON the evening of the 19th December 1849, whilst walking 
near the southern part of Edinbiirgli, about fifteen mi- 
nutes past five, Greenwich time (as I afterwards estimated), 
I observed a meteor, fully brighter than Venus at her average 
brilliancy, moving from W. towards N., parallel to the horizon, 
elevated 15° above it, and followed by a distinct luminous 
train. This angle was subsequently taken by estinuition by 
daylight, with the aid of a theodolite; an<l the compass-bear- 
ing of the meteor, when first seen, ascertained in the same 
way, must have been 47^ W. of N. When it bore 29^ E. of 
magnetic north, it was observed to have divided into two, the 
one part following the other at some distance; and I soon 
after lost sight of it in the obscurity of the smoke of the town. 
When it split, its altitude was estimated at 6°. It thus de- 
scribed an arc of no less than 76^, in doing which it occu- 
pied, as I roughly estimated, about fifteen seconds, or possibly 

Having sent a short notice of the appearance of the meteor 
to the Courant newspaper, I received from many quarters 
accounts of its having been seen under circumstances remark- 
ably similar to those just described. I believe that nearly 
forty communications on the subject have reached me from 
places included between Longford, in the centre of Ireland, to 
near Bervie in Kincardineshire, a distance of above 300 miles, 
in a direction nearly N.E. and S.W. ; whilst in a perpendi- 
cular direction, or I'rom N.W. to S.E., the range of observa- 
tion has been comparatively small ; lor I have received no 
information from beyond Renfrew in the one direction, and 
Durham in the other, .being about 140 miles distant in a 
straight line. The meteor vvas seen at Longford, in Ireland, 
74 miles west of Dublin, but not in Dublin itself. It was 
seen at Belfast, between Carlisle and Gretna at Stewarton in 
Ayrshire, at Johnstone, at Paisley, Renfrew, and by many 
persons in Glasgow and the neighbourhootl. It was also 
generally seen in Edinburgh, in East Lothian, near Melrose, 
and at Durham, as already mentioned. Further north, I have 
received accounts from Crail, St. Andrews, Dundee, Perth, 
and Johnshaven to the north of Montrose. 

The greater number of these communications concur in 
estimating the direction of the motion of the meteor to have 
been from S.W. to N.E., although, as might be expected, 

* From the Proceedings of the Royal Society of Edinburgh, vol. ii. 
No. 39. 

358 Prof. Forbes's Account of a remarkable Meteor^ 

they vary excessively as to its distance and magnitude; being 
described by some persons as only 50 or 100 yards off, and 
as large as the moon ; by others, as a ball of 9 inches in dia- 
meter, or the size of a large egg. One person only professes 
to have heard a sound. The time during which it was seen 
was variously estimated. At Longford, by Mr. Curtis, 20 
seconds ; at Glasgow, by Mr. Stevenson, at 20 seconds ; at 
Johnstone, by Mr. Cunningham, 15 seconds; at Perth, 15 
or 20 seconds; at Durham, by Mr. Carrington, 30 seconds; 
at St. Andrews, 15 seconds according to one observer, and 
18 to 21 seconds according to another; at Johnshaven, ^ths 
of a minute. The hour of the appearance of the meteor, in 
most of the descriptions, is stated at between 5^ 10'" and 5^16"^. 

The arc of the horizon which it was seen to traverse de- 
pended, of course, on the point where the meteor first caught 
the observer's eye. At Granton, it was traced by Professor 
Kelland through 125° of azimuth ; at Perth, 130°; at St. An- 
drews, 74-°; at Edinburgh, 76°; at Durham, Qb"^ -^ at Glas- 
gow, from 60° to 70°. The division of the head or nucleus 
into several parts, and, first of all (in most cases), into /too, has 
been noticed with remarkably slight variation ; consequently, 
the explosion of the meteor marks a well-determined point in 
its path. The separation was specially noticed at Edinburgh, 
Granton, Glasgow, Renfrew, Melrose, Haddington, Johns- 
haven, Perth, Durham and St. Andrews. 

In a majority of cases a luminous train was observed ; and 
I am confident that the existence of this train, which has been 
estimated at from 2° to 3° long, cannot be questioned. Dr. 
Adamson, however, especially remarked that no train was to 
be seen at St. Andrews. 

On revising the whole accounts, it does not appear that any 
of them can be relied upon for ascertaining the position of 
the meteor in space, except the observations of Mr. Carring- 
ton of the Durham observatory; of Professor Kelland, Mr. 
Stirling and myself, at Edinburgh; of Dr. Adamson and an- 
other observer, communicated by Professor Fischer of St. 
Andrews; of a young gentleman at Perth, communicated by 
Thomas Miller, Esq., Rector of the Perth Academy ; and of 
A. D. Stevenson, Esq., and \V. Gourlie, Esq., jun., at Glas- 
gow. My inquiries were chiefly directed to the two following 
points '. Jirst, the angular elevation of the meteor in the N.W, 
quarter of the lieavens, where it is admitted by all that its 
path appeared almost horizontal ; secondly, to the bearing of 
the meteor at the instant of explosion. 

At Durham, Mr. Carrington saw the meteor first when the 
bearing was true N.W., the altitude (by theodolite) was then 

seen December 19, 184'9. 359 

10°, or not exceeding 11°; when it burst it was due N. (true), 
and continued to move 10° or 12° f'urtiier before it disap- 
peared. Professor Chevallier, who obligingly communicated 
these results, states that the meteor appeared rather to rise as 
it approached the north, but with a doubt. This supposition, 
however, appears inadmissible, from the unanimity of the 
other accounts. 

At Granton, near Edinburgh, Professor Kelland caught 
sight of the meteor a little to the N. of the moon, and several 
diameters below it. This corresponds, by after estimation 
with a theodolite, to 75^ W. of magnetic N., and an altitude 
of 12°. Professor Kelland thinks that it rather rose after- 
wards. It split into two at 20° E. of magnetic N., having 
then an altitude of only 5°; it continued for a considerable 
time bright, then began to fade, as if by the effect of distance, 
and also to separate into several parts : it was finally lost sight 
of 50° E. of magnetic N. (this bearing is well ascertained), 
with an altitude estimated at only half a degree. The position 
and circumstances of these observations, made at an elevated 
station above the Frith of Forth, were eminently favourable. 

Mr. J. Stirling, civil engineer, looking up North Hanover 
Street, Edinburgh, saw the meteor separate into two parts ; 
the bearing; he afterwards estimated at 25° E. of magnetic N. 
(the probable error not exceeding 1 ), and the altitude at 
8° 30', certainly not exceeding 9°. 

I think we may conclude, that at Edinburgh the meteor 
attained a maximum elevation of 15° (that mentioned in the 
commencement of this paper), since it no doubt rose after 
Professor Kelland first saw it to the S. of the true W., with 
an altitude of only 12°. The course of the meteor was evi- 
dently such as to be nearest the spectator when in the true 
N.W. or W.N.W. 

The place of the meteor when it burst stands thus: — 

Kelland, N. 20° E. (mag.) Alt. 5°. 
Stirling, N. 25° E. Alt. 8° 30'. 

Forbes, N. 29° E. Alt. 6°. 

The average is almost 25° E. of N., or about 1° W. of the 
true meridian, the variation being nearly 26°. The mean of 
the three observations of altitude would be6°30'; but admit- 
ting Mr. Stirling's to be entitled to the greatest confidence, 
we may suppose it 7°, or possibly a little more. 

At St. Andrews, the meteor was seen by Dr. Adamson, 
when riding in a northerly direction on the Largo road. Pro- 
fessor Fischer was so kind as to accompany him afterwards 
to the spot, and to reduce his observations with all the accuracy 

360 Prof. Forbes's AccouiU of a remarkable Meteor, 

of which they were capable. It was first noticed when bear- 
ings,',' ^^^ of mngnellc N., and disappeared at42,y°E. of N.; 
the altitude was conjecturally stated as between 11° and IS^^^ 
and it appeared to move horizontally, but rather declining 
towards the N. 

After describing three-fourths of its course, it split into two 
parts, which went on close together lor a little, then broke 
into four or five, became dull red, and rapidly disappeared; 
the separate {pieces travelling on together until tiie last. 

Another intelligent observer near St. Andrews, whose evi- 
dence was taken by Mr. Fischer, first saw the meteor 29 j" W. 
of magnetic N., and estimated the point where the meteor 
burst at ^^^ E. of N; but this last number coincides so closely 
with Dr. Adamson's estimate of the point of final disappear- 
ance, that it is perhaps allowable to suppose, that this second 
observer had mixed up these two events in his description. 
Dr. Adamson's statement, that one-fourth of the arc which 
he saw was described after the meteor had split, would give 
an azinnith at that moment of almost 30^ E. of N. magnetic, 
or 4-° E. of N. true, as Mr. Fischer determined the magnetic 
declination to be about 25° 46'. The altitude of the meteor, 
as seen by this observer, appears not to have exceeded 15° 
(the same as at Edinburgh) ; which number we shall therefore 

At Perth, the passage of the meteor was seen from the 
North Inch, by a young gentleman of intelligence, whose ob- 
servations were reduced to numbers by Mr. Miller, Rector of 
the Perth Academy, who was so good as to accompany him 
to the spot, and take the angles with a theodolite. Its bear- 
ing, when first seen, was 46 S. of W. true ; its angular alti- 
tude was at that time only 3° 30'. This is by far the most 
southern azimuth which has been observed. Its bearing, 
when it disappeared, was 6° W. of N., but it was then lost in 
a cloud. If I understand right, it had by this time separated 
into fragments. Its apparent altitude in the middle of its 
course was about 17° 3C'. These observations, extending 
over an arc of 130°, taken along with Professor Kelland's, 
clearly demonstrate that the meteor appeared with a very low 
altitutle in the S.W. quarter of the heavens, and disappeared 
in a similar way in the N.N. E., attaining its greatest elevation 
about W.N.W. (true). 

At Glasgow the meteor was very generally and well seen. 
Mr. William Gourlie, jun., saw it move from S.W. to N.N.E., 
over an arc of 60" or 70"^, and divide into two, when it bore 
40° E. of magnetic N. He estimates its greatest elevation at 
30° ; and that it decreased to between 15° and 1 7°, or even 

seen December 19, IS^O. 


less at the time of its separation : he adds, that he is not much 
accustomed to such observations. Mr. A. D. Stevenson, 
living in South Portland Street, Glasgow, saw the meteor 
moving along at a height just sufficient to clear the chimney- 
tops, on the west side of the street; an elevation which he 
afterwards estimated, as he states, with considerable accuracy 
at 28°. I have I'eceived further and more minute accounts of 
the appearance of the meteor from Mr. Stevenson, wlio lias 
been most kind and intelligent in his communications ; and 
my friend Mr. James Peddie has verified the accuracy of Mr. 
Stevenson's observations beyond the possibility of mistake. 
It appears that the meteor passed quite clear of a stack of 
chimneys on the opposite side of the street, which would give 
it a well-defined minimum altitude of 25^ 41'; but Mr. Ste- 
venson is of opinion that it rose more than 2-' higher, or to 
not less than 28^ (perhaps even to 28° 21'); when it was 
highest, its bearing was .52|^° W. of N. (magnetic), and it dis- 
appeared from his view when it bore 40^ 27' E. of magnetic 
N. It was then decidedly single. Now this bearing coincides 
with that at which Mr. Gourlie observed it to become double, 
and consequently the limit towards the N. of this event is se- 
verely defined. 

The followinij table contains the most definite of these ob- 
servations, and the azimuths are all reduced to the true me- 


True azi- 
muth when 
first seen. 

True azimuth 
of disappear- 


True azimuth 
of first ex- 


at first 


Durham . . . 
St. Andrews 

Glasgow . . . 

10° 30 
17 30 




W. 47° S. 

N. 12° E. 
N. 24° E. 
N. 16° E. 
N. 7°W. 
(in a cloud) 




N. 1° W. 
N. 4° E. 

N. 14° E. 


Remarks on the Observations. 

1. On the whole, these observations are not consistent, and 
cannot (I conceive) be cleared up without additional and accu- 
rate ones, which it may now be too late to procure. The 
central group of stations, Edinburgh, Perth and St. Andrews, 
are sufficiently accordant, and indicate that the path of the 
meteor must have been nearly parallel to a line passing 
through the first and last of those places, or in a direction N. 
27^ E. (true) ; which accords well with the observations at 
most of the individual stations, and particularly with the vcc- 

362 Prof. Forbes's Accoimt of a remarkable Meteor. 

nishiug direction in Professor Kellaiid's remarkable observa- 
tion at Granton. 

2. Tile Diirliam observation is compatible with the above- 
mentioned iridup within the limits of error. By the combina- 
tion of Dmham and Edinburjrji (the base line perpendicular 
to the assumed direction of the meteor's motion being ninety- 
five miles), I calculated that the meteor passed vertically nearly 
over the Island of St. Kilda, with an absolute elevation of 
about eighty-eight miles. But this solution seems absolutely 
excluded by observations at Glasgow which admit of no ques- 
tion, and which 1 have spared no jiains in verifying. Had 
the position of the meteor been such as I have first assumed, 
it could not possibly have been seen over even the roofs of the 
houses from the station occupied by Mr. Stevenson, much less 
over the chimney-tops. The bearing at the moment of ex- 
plosion at Glasgow, also singularly enough corroborates suf- 
ficiently well the comparatively small elevation (about twenty 
miles above the earth) which the combination of Edinburgh 
and Glasgow gives ; and this bearing we have seen to have 
been also accurately defined by the physical obstacles bound- 
ing the observer's view ; it would have given a parallax of 15°, 
subtended by the perpendicular on the meteor's path, referred 
to Glasgow and Edinburgh respectively. Now, if this calcu- 
lation were anything like correct, the Perth observation is 
entirely wrong; and the meteor could not have risen about 
6^ above the horizon of Durham, instead of 10° or 1 1° as esti- 
mated. I am unable in any degree to explain these conflicting 

y. The observations of Professor Kelland at Granton, and 
those at Perth, throuuh the great azimuths of 125° and 
1:50°, described by the meteor with such remarkable delibe- 
ration of motion, lead, when analysed, to the very same results 
which presented themselves to the mind of the spectator in- 
tuitively ; namely, that the motion must have been sensibly 
rectilinear, equable, and parallel to the horizon at Edinburgh. 
Assuming that the greatest altitude at Edinburgh was 15°, 
and the bearing then N. 63° W. (true), we may calculate that 
the altitude should have been on this hypolhesi?, when first 
seen by Professor Kelland, 11° 47', instead of 12° as observed; 
at explosion, 6° 59' (7° observed), and at its final disappear- 
ance 0° 47' (instead of 0° 30' observed). Again, at Perth, the 
observed altitude, when first seen, was 3^^°, and the calculated 
altitude 5° 3', taking the maximum altitude at 17^°. The 
coincidence is, on the whole, remarkable; though it would be 
rash to push it to an extreme, as an error of some degrees 
may exist in the assumption of the direction of the meteor's 

Mr. J. J. Sylvester 07i a new Class of Theorems. 363 

course. Some later observations, received from Mr. Curtis 
at Longford, and a consideration of the effects of perspective 
at Perth and Edinburgh, incline me to admit that the path 
might make an angle 3° or 4° greater with the meridian than 
I have above supposed. These conclusions are independent 
of the actual distance or parallax of the meteor; which, as I 
have said, cannot be determined without further observations, 
which I should be glad to receive from any quarter, but more 
particularly from Ireland, and from the centre and N.W. of 
Scotland. If correct, they entitle us to infer that the meteor 
in question was most probably a body moving in space, in a 
path little curved, and not revolving round the earth. 

XLVII. Additions to the articles in the September Number of 
this Journal, " On a nevo Class of Theorems " and on Pascal's 
Theorem. By J. J. Sylvester, M.A,, F.R.S.* 

THIRST addition. — I have alluded in the above article to a 

more general theorem, comprising, as a particular case, 

the theorem there given for the simultaneous evanescence of 

two quadratic functions of 2« letters, or n linear equations 

becoming instituted between the letters. 

In order to make this generalization intelligible, I must 
premise a few words on the Theory of Orders, a term which 
I have invented with particular reference to quadratic func- 
tions, although obviously admitting of a more extended appli- 
cation. A linear function of all the letters entering into a 
function or system of functions under consideration I call an 
order of the letters, or simply an Order. Now it is clear that 
we may always consider a function of any number of letters 
as a function of as many orders as there are letters ; but in 
certain cases a function may be expressed in terms of a fewer 
number of orders than it has letters, as when the general 
characteristic function of a conic becomes that of a pair of 
crossing lines or a pair of coincident lines, in which event it 
loses respectively one and two orders, and so for the charac- 
teristic of a conoid becoming that of a cone, a pair of planes 
or two coincide;. t planes, in which several events, a function 
of four letters, becomes that of only three orders, or two 
orders, or one order, respectively. When a function may be 
expressed by means of r orders less than it contains letters, I 
call it a function minus r orders. I now proceed to state my 

Let U and V be functions each of the same m letters, and 

* Communicated by the Author. 

se^ Mr. J. J. Sylvesler on a new Class of Theorems. 

suppose tlmt tlii; determinant in respect of those letters of 
U + /iV contains / pairs of equal linear factors of ^u, ; then it is 
possible, by means off linear ecjuations instituted between the 
letters, to make U and V each become functions of the same 
VI — 2i orders; and conversely, if by i equations between the 
letters U and V may be made functions of the samem—'-Zi 
orders, the determinant of U + yu-V considered as a function of 
fjb will contain / quadratic factors. 

Tims when m=i2n and ?' = ??, U and V will each become 
functions of zero orders, /. e. will both disappear, provided 
that on llie institution of a certain system of // linear equations, 
among the letters of which U and V are functions, the deter- 
minant of (U + /aV) is a perfect square, — which is the theorem 
given in the article referred to. 

80 [ex. gr.) if U and V be quadratic functions of four letters, 
and therefore the characteristics oftwo conoids, | [ (U + yitV) 
being a perfect square, expresses that these conoids have a 
straight line in common lying upon each of their surfaces. 

If U and V be quadratic functions of three letters only, and 
admit therefore of being considered as the characteristics of 
two conies, ' |(U-f jtiV) containing a square factor, is indi- 
cative of these conies having a common tangent at a common 
point, /. e. of their touching each other at some point; for it 
is easily shown that the disappearance of two orders from any 
quadratic function by virtue of one linear function of its letters 
being zero, indicates that the line, plane. Sec. of which the 
linear function is the characteristic is a tangent to the curve, 
surface, &c. of which the quadratic function is the character- 

I pass now to a generalization of the theorem which shows 
how to express, under the form of a double determinant, the 
resultant of one linear and two quadratic homogeneous func- 
tions of three letters (which I should have given in the original 
paper, had I not there been more intent upon developing an 
ascending scale than of expatiating upon a superficial ramifi- 
cation of analogies), and which constitutes my Seco?id addition 
to that paper, to wit — 

If U and V be homogeneous quadratic, and Lj L^ . . . .L« 
homogeneous linear functions of {n-\-2) letters x^ x^. . . . x^+2i 
the determinant of the entire system of n + 2 functions is equal 

the demonstration is precisely similar to the analytical one 

Mr. J. J. Sylvester on a nexv Class of Theorems. 365 

given in tlie September Number for the particular case of 

When ;i = 0, we revert to Mr. Boole's theorem of elimina- 
tion between U and V already adverted to. The proof, it 
will be easily recognized, does not require the application of 
the more general theorem relative to the simultaneous de- 
pression of orders of two quadratic functions, but only the 
limited one before given, which supplies the conditions of their 
simultaneous disparition. 1 now proceed to develope more 
particularly certain analogies between the theory of the mutual 
contacts ot tvvo conies, and that of the tangencies to the inter- 
section of two conoids. 

But here again I must anticipate some of the results which 
will be given in my forthcoming memoir on Determinants and 
Quadratic Functions, by explaining what is to be understood 
by minor determinants, and the relation in which they stand 
to the complete determinant in which they are included. This 
preliminary explanation, and the statement of the analogies 
above alluded to, will constitute my Third and last addition. 

Imagine any determinant set out under the form of a square 
array of terms. This square may be considered as divisible 
into lines and columns. Now conceive any one line and any 
one column to be struck out, we get in this way a square, one 
term less in breadth and depth than the original square ; and 
by varying in every possible manner the selection of the line 
and colunui excluded, we obtain, supposing the original square 
to consist of n lines and n colunms, w- such minor squares, 
each of which will repre^ent what I term a First Minor Deter- 
minant relative to the principal or complete determinant. 
Now suppose two lines and two columns struck out Irom the 

original square, we shall obtain a system of -| - — V 

square?, each two terms lower than the principal square, and 
representing a determinant of one lower order than those 
above referred to. These constitute what I term a system of 
Second Minor Deterrmnants; and so in general we can form 
a system of rth minor determinants by the exclusion of/- lines 
and r columns, and such system in general will contain 

{n-\)....{n-r+\ )\'^ 
1.2 r J 

distinct determinants. 

1 say ^in general;' because if the principal determinant be 
totally or partially symmetrical in respect to either or each of 
its diagonals, the number of distinct determinants appertaining 
to each system of minors will undergo a material diminution, 
which is easily calculable. 


366 Mr. J. J. Sylvester on a new Class of Theorems. 

Now I have established the following law: — 
The wiiole of a system of ;th minors being zero, implies 
only (?•+ 1)- equations, i. e. by making (r+ I)- of these minors 
zero, all will become zero ; and this is true, no matter what 
may be the dimensions or form of the complete determinant. 
But furtiiermore, if the complete determinant be formed from 
a quadratic function, so as to be symmetrical about one of its 

diagonals, then ^ — —~ only of the rth minors being 

zero, will serve to imply that all these minors are zero. Of 
course, in applying these theorems, care must be taken that 

the (;■+ 1)- or ~ selected equations must be mutu- 
ally non-implicative, and shall constitute independent condi- 

In the application I am about to make of these principles, 
we shall have only to deal with a system ofjirst minors and of 
a symmetrical determinant. If three of these properly selected 
be zero, from the foregoing it appears that all must be zero. 

Now let U and V be characteristics of two conies, i. e. let 
each be a function of only three letters, it may be shown (see 
my paper in the Cambridge and Dublin Mathematical Journal 
for November 1850) that the different species of contacts be- 
tween these two conies will correspond to peculiar properties 
of the compound characteristic U + /U.V. 

If the determinant of this function have two equal roots, the 
conies simply touch; if it have three equal roots, the conies 
have a single contact of a higher order, i. e. the same curva- 
ture; if its six first minors all become zero simultaneously for 
the same value of//-, the conies have a double contact. If the 
same value of yu,, which makes all these first minors zero, be 
at the same time not merely a double root (as of analytical 
necessity it always must be), but a treble root of 

|— I (U +,/.¥) = 0, 

then the conies have a single contact of the highest possible 
order short of absolute coincidence, i. e. they meet in four 
consecutive points. 

The parallelism between this theory and that of two qua- 
dratic functions P, Q,and one linear function L* of four letters, 
say x^ j/, ;::-, ^, is exact t. For let P+Lw + /-tQ be now taken 

* Observe that P=:0, Q==0, L=:0 now express the equations to two co- 
noids and a plane respectively. 

■\ This parallelism may be easily shown analytically to imply, and be 
implied, in the geometrical fact, that the contact of the plane L with the 
intersection of the two surfaces P and Q, is of exactly the same kind as the 
contact (which must exist) between the two conies which are the intersec- 
tions of P and Q respectively with the plane L. 

Mr. J. J. Sylvester on a new Class of TJieorems. 367 

as our compound characteristic (a function, it will be observed, 
of five letters, .r, ?/, ,;r, t, u) ; if its determinant have two equal 
roots, L has two consecutive points in common with the inter- 
section of P and Q, /. e. passes through a tangent to that in- 
tersection ; if it have three equal roots, L has three consecu- 
tive points in common with the said intersection, i. e. is an 
osculating plane thereto; if its fifteen first minors admit of all 
being made simultaneously zero, L has a double contact with 
the intersection of P and Q, i. e. it is a tangent plane to some 
one of the four cones of the second order containing this in- 
tersection; if the same linear function of /a which enters into 
all these first minors be contained cubically in the complete 
determinant, then the plane L passes through four consecutive 
points of the intersection of P and Q, and the points where it 
meets the curve will be points of contrary planeflexure; and, 
as it seems to me, at such points tiie tangential direction of 
the curve must point to the summit of one or the other of the 
four cones above alluded to*. In assigning the conditions for L 
being a double tangent plane to the intersection of P and Q, 
we may take any three independent minors at pleasure equal 
to zero. One of these may be selected so as to be clear of 
the coefficients of L ; in fact, the determinant of P + z^tQ will 
be a first minor of P + yu-Q + Lw ; /* may thus be determined 
by a biquadratic equation ; and then, by properly selecting 
the two other minors, we may obtain two equations in which 
only the first powers of the coefficients of a*, ^, s, t in L appear, 
and may consequently obtain L under the form of 

{ae-\-a)x-\-{he + ^)2j-\-[ce + r^)z-\-{de + h)t, 

where «', «; h, ^•, c, 7; d, h will be known functions of any 
one of the four values of /it. The point of contact being given 
will then serve to determine e, and we shall thus have the equa- 
tion to each of the four double tangent planes at any given 
point fully determined. 

In the foregoing discussions I have freely employed the 
word characteristic without previously defining its meaning, 
trusting to that being apparent from the mode of its use. It 
is a term of exceeding value for its significance and brevity. 
Thecharacteristicof a geometrical figure f is thefunction which, 

* If this be so, then we have the following geometrical theorem : — " The 
summit of one of Uiefonr cones of the second degree which contain the inter- 
sections of two surfaces of the second order drawn in any manner respectively 
through tivo given conies tying in the same jitane, and having with one another 
a contact of the third degree, ivill always be found in the same rigtit line, 
namely in the tangent tine to the two given conies at tlie point of contact." 

f More generally, the characteristic of any fact or existence is tlie fiinc- 

36S Mr. J. J. Sylvester on it luiv Class of Theorems. 

equaled to zero, coiistllutes the ocjiiatioii to siidi figure. 
Pliicker, I think, somewhere calls it die line or sin face func- 
tion, as the case may be. Geometry, analytically considered, 
resolves itself into a system of rules for the construction and 
interpretation of characteristics. One more remark, and 1 
have done. A very comprehensive theorem has been given 
at the conm^encement of this commentary, for interpreting 
the elf'ect of a com))le(e determinant of a linear function ot two 
(juadralic functions (U+/LiV), having one or more pairs of 
equal factors (c + e/i). But liere a tar wider theory |>resents 
itself, of which the aim should be to determine the effect and 
meaning of this determinant, having any amount and distri- 
bution of multiplicity whatsoever among its roots. Nor must 
our investigations end at that j)oint; but we must be able to 
determine the meaning and effect of common factors, one or 
more entering into the successive systems of minor determi- 
nants derived from the complete determinant of U+yu,V. 

Nor are we necessarily confined to two, but may take several 
quadratic functions simultaneously into account. 

Aspiring to those wide generalizations, the analysis of qua- 
dratic functions soars to a pitch from whence it may look 
proudly down on the feeble and vain attempts of geometry 
proper to rise to its level or to emulate it in its flights. 

2Q Lincoln's-Inn-Fields, 
September 3, 1850. 

The law which I have stated for assigning the number of 
independent, or to speak more accurately, non-coevanescent 
determinants belonging to a given system of minors, I call 
the Homaloidal law, because it is a corollary to a proposition 
which represents analytically the indefinite extension of a pro- 
perty common to lines and surfaces to all loci (whether in 
ordinary or transcendental space) of the first order, all of 
which loci may, by an abstraction derived from the idea *of 
levelness common to straight lines and planes, be called Ho- 
maloids. The property in cjuestion is, that neither two 
straight lines nor two planes can have a common segment ; in 

tion which, equaled to zero, expresses the condition of the actuality of such 
fact or existence. 

Perhaps the most important pervading principle of modern analysis, but 
which has never hitherto been articulately expressed, is that, accorrling to 
which we inter, that when one fact of whatever kind is implied in another, 
the characteristic of the first must contain as a factor the characteristic of 
the second ; and that when two facts are mutually involved, their charac- 
teristics will be powers of the same integral function. 

The doctrine of characteristics, applied to dependent systems of facts, 
admits of a wide development, logical and analytical. 

Mr. J. J. Sylvester on a next) Class of Theorems. ZQ^ 

other words, if ?i iiulej^endent relations of rectilinearity or of 
coplanarity, as the case may be, exist between triadic gronps 
of a series of /i + 2, or between tetradic gronps of a series of 
« + 3 points respectively, tlien every triad or tetrad of the 
series, accordintf to the respective suppositions made, will be 
in rectilinear or in plane order. So, too, if n independent 
relations o\ coincidence exist between the duads formed out of 
iL-{-\ points, every duad will constitute a coincidence. 

This homaloidal law has not been stated in the above com- 
mentary in its form of greatest generality. For this purpose 
we must commence, not with a square, but with an oblong 
arrangement of terms consisting, suppose, of ?« lines and n 
columns. This will not in itself represent a determinant, but 
is, as it were, a Matrix out of wliich we may form various 
systems of determinants by fixing upon a number ^j, and se- 
lecting at will p lines and p columns, the squares corresponding 
to which may be termed determinants of theyjth order. We 
have, then, the following proposition. The number of unco- 
evanescent determinants constituting a system of the pth order 
derived from a given matrix, n terms broad and m terms deep, 
may e(jual, but can never exceed the number 


Repurk on Pascal's and Brianchon's Theorems. 

I omitt :\ to state, in the September Number of the Journal, 
that the temonstration there given by me for Pascal's, ap- 
plied equally to Brianchon's theorem. This remark is of 
the more importance, because the fault of the analytical de- 
monstrations hitherto given of these theorems has been, that 
they make Brianchon's a consequence of Pascal's, instead of 
causing the two to flow simultaneously from the application 
of the same principles; No demonstration can be held valid 
in method, or as touching the essence of the subject-matter, 
in which the indifference of the duadic law is departed from. 
Until these recent times, the analytic method of geometry, as 
given by Descartes, had been suffered to go on halting as it 
were on one foot. To Pliicker was reserved the honour of set- 
ting it firmly on its two equal supports by supplying the com- 
plementary' system of coordinates. This invention, however, 
had become inevitable, after the profound views promulgated 
by Steiner, in the introduction to his Geometry, had once taken 
hold of the minds of mathematicians. To make the demon- 
stration in the article referred to apply, tolidem Uteris, to 
Brianchon's theorem (recourse beins: had to the correlative 
system of coordinates), it is only needful to consider U as the 

Phil. Ma'T. S. 3. Vol. 37. No.' 251. Nov. 1850. 2 B 

370 Mr. J. J. Sylvester oji the sohition of 

characteristic of the tangential envelope of the conic, .r, ?/, z^ t, 
ti, V as the characterislics of the six po\nts o( the circumscribed 
hexagon, (j) the characteristic of the point in which the line 
Xf V meets the line z^ t; ay — am will then be shown to cha- 
racterize the point in which t^ x meets f, ;::; and thus we see 
that y^ u\ t, x; i', z, the three pairs of opposite sides of the 
hexagon, will meet in one and the same point, which is Brian- 
chon's theorem. 

XLVIII. 0?i the solution of a System of Equations in isohich 
three Homogeneous Qiiadratic Functions of three tmkno'wn 
quantities are respectively equaled to numerical Midtiples 
of a fourth N on- Homogeneous Function of the same. By 
J. J. Sylvester, M.A., F.ll.S.^^ 

LET U, V, W be three homogeneous functions of a, ^, z, 
and let o) be any function of a-, j/, z of the ?/th degree, 
and suppose that there is given for solution the system of 

U = A.a) 

V = B.« 


Theorem. — The above system can be solved by the solution 
of a cubic equation, and an equation of the //th degree. 
For let D be the determinant in respect to x^ y^ z of 

then D is a cubic function of/, g, h. Now make D = 

A/+Bo + CA=0, 

the ratios of/: g : h which satisfy the last two equations can 
be determined by the solution of a cubic equation, and there 
will accordingly be three systems of/, g, h which satisfy the 
same, as 

/i 5i ^^1 

A g^ K 

/s ^3 ^3- 

Now D = implies that/U+^V + AW breaks up into two 
linear factors; accordingly we shall find 

{l^x + m^y + x^z) . (Xja? + ix^y + v^z) — 

{l^^m^y-^x^z) (X3a; + /A3?/ + j/32') = 0, 
* Communicated by the Author. 

a System of Equations. 371 

in which the several sets of/, ;«, ii; X, fu,, v can be expressed 
without tUfficuUy in terms of the several values of v^/, V g, \/h. 
Let the above equations be written under the form 

PP' = 

Since the given equations are perfectly general, it is readily 
seen that the equations 

(P=o P'=o) (Q=o Q'=o) (R=o R'=o) 

will severally represent pairs of opposite sides of a quadrangle 
expressed by general coordinates ,r, y, ::', so that one of the 
two functions R, R' will be a linear function of P and Q and 
also of P' and Q', and the other will be a linear function of P 
and Q' and also of P' and Q *. 

In order to solve the equations, we need only consider two 
such pairs as PP' = QQ' = 3 we then make 

P = Q=0, 

P=0 Q' = 0, 

P' = Q = 0, 

P'=0 Q' = 0. 

Any one of these four systems will give the ratios o^ x x y : zi 
and then, by substitution in any one of the given equations, 
we obtain the values of a-, y, z by the solution of an ordinary 
equation of the wth degree. The number of systems x^ y, z 
is therefore always 4n. 

The equations connected with the solution of Malfatti's 
celebrated problem, " In a given triangle to inscribe three 
circles such that each circle touches the remaining two circles 
and also two sides of the triangle," given by Mr. Cayley in 
the November Number for 1849 of the Cambridge and Dublin 
Mathematical Journal, to wit, 

bf + c^2 _^ 2fyz = d\ a {he -P) = A 

c^^-{-asc''' + 2gzx=6-\b{ca-g'^) = B 

ax^ + 6/ + 2hxy = OK c{ab- Ji^) = C, 

* Were it not for this being the case, the number of solutions would be 
n times the number of ways of obtaining duatls out of tbree sets of two 
things, excluding the duads fornn'ng the sets, i. e. the number of solutions 
would be \2n in place of 4n, the true number. 

2 B 2 

S72 On I he sol id ion of a System of Equations. 

come under llie general lorni which has just been solved. It 
^o happens, however, that in this particuhir case 

become respectively 






h > 






1 -| 
■ C 






and the cubic equation is resolved without extraction of roots. 
It follows irom my theorem that the eight intersections of 
three concentric surfaces of the second order can be found 
by the solution of one cubic and one quadratic equation; and 
in general, if we have ^, -v/^, any three (juadratic functions 
of .r, ^, ~, and ^ = 0, -^ = 0, 6 = be the system of equations 
to be solved, provided that we can by linear transformations 
express </>, -v/^, 6 under the form of 

JJ — a'w 


W — cw, 

U, V, W being homogeneous functions, and w a non-homo- 
geneous function of three new variables, a.', y, s', we can find 
the eight points of intersection of the three surfaces, of which 
U, V, W are the characteristics, by tiie solution of one cubic 
and one quadratic. But (as I am indebted to Mr. Cayley for 
remarking to me) that this may be possible, implies the coin- 
cidence of the vertices of one cone of each of the systems of 
four cones in which the intersections of the three surflices 
taken two and two are contained. 

I may perhaps enter further hereafter into the discussion of 
this elegant little theory. At present 1 shall only remark, 
that a somewhat analogous mode of solution is applicable to 
two equations, 



in which U, V are homogeneous quadratic functions, and P 
some non-homogeneous function oi'x,y. 

We have only to make the determinant ofyU-j-^^V equal 

On the Meteorology of England and the South of Scotland. 373 

to zero, and we shall obtain two systems of" values of/, g^ 
w herefrom we derive 

l^x + m,ij=± \^af^ + bg^ . P 

l-^r + m.2^= ± \^ af\ + hg^ . P, 

from which .v and j/ may be determined. 

26 Lincoln's-Inn-Fields, 
August 28, 1850. 

XLIX. On the Meteorology of England and the South of Scot- 
land during the Quarter ending September 30, 1850. By 
James Glaisheh, Esq.^ F.R.S., Hon. Sec. of the British 
Meteorological Society, c^r.^'' 

THE mean daily temperature of the air was below its ave- 
rage value till July 13; the mean defect was 2°'2. From 
Julj' 12 to the 24th, the period was warm ; the average excess 
of temperature was 4'°'S. From July 25 to August 3, the 
temperature was below the average; its mean deficiency was 1°. 
From August 4 to August 18, it was above the average ; the 
mean excess was 2^ ; this was followed by a long period of fine, 
clear, dry, but cold weather. The average deficiency of tem- 
perature between August 19 and September 1 7 was 3^'5 ; and 
after September 18, the daily temperatures were slightly above 
their average values. Snow fell on Ben- Lomond on August 23. 

The mean temperature of the air at Greewwich for the three 
months ending August, constituting the three summer months, 
was 6l°'l, being 1°*2 above the average of the preceding 
seventy-nine sunnners. 

For the month of July was 62°'2, exceeding that of the ave- 
rage of seventy-nine years by 0°'9,and of nine years by 0*^*7. 

For the month of August was 60'^*2, being 0°*3 less than 
the average of seventy-nine years, and "9 less than that of the 
preceding nine years. 

For the month of September was 56°'4, exceeding the ave- 
rage from seventy-nine years l)y 0"*1, and less than that of 
the preceding nine years by 0°'7. 

The mean for the quarter was 59'"6, exceeding that of the 
average of seventy-nine summer quarters by "2, and less 
than that of the nine preceding years by 0°'3. 

The mea7i temperature of evaporation at Greenisoich — 

For the month of July was 58°'6 ; for August was 56'^'6 ; 
and for June was 52 "9. These values are 0°*9 greater, 0°'2 
greater, and 1°"6 less than those of the averages of the same 
months in the preceding nine years. 

* Comnninicated by the Author. 

ST-t Mr. J. Glaisher on the Mctcorologi/ of England 

The mean temperature of the de'tv-poitU at Grcetiwich — 

For the months of July, August and September, were 55''*8, 
53"* 1, and 47°'7 respectively. These values are 1°- 5 greater, 
2^'0 less, and 4°-7 less respectively than the averages of the 
same months in the preceding nine years. 

The 7)ica?/ elastic force of vapour at Greeii'doich for the quarter 
was 0'422 inch, being less than the average from the preceding 
nine years by 0"OOS inch. 

The mean tve